What is the “lowest energy”?











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In many textbooks I come across the term lowest energy. For example in atomic structures, electrons are placed in orbitals in order for the atom to have the lowest energy. But what is this energy? Potential- or kinetic energy or the sum of the two?






quantum-mechanics energy hilbert-space ground-state







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    The sum of the two, usually the eigenvalue of the Hamiltonian operator.
    – Lewis Miller
    11 hours ago















up vote
3
down vote

favorite












In many textbooks I come across the term lowest energy. For example in atomic structures, electrons are placed in orbitals in order for the atom to have the lowest energy. But what is this energy? Potential- or kinetic energy or the sum of the two?






quantum-mechanics energy hilbert-space ground-state







share|cite|improve this question




















  • 4




    The sum of the two, usually the eigenvalue of the Hamiltonian operator.
    – Lewis Miller
    11 hours ago













up vote
3
down vote

favorite









up vote
3
down vote

favorite











In many textbooks I come across the term lowest energy. For example in atomic structures, electrons are placed in orbitals in order for the atom to have the lowest energy. But what is this energy? Potential- or kinetic energy or the sum of the two?






quantum-mechanics energy hilbert-space ground-state







share|cite|improve this question















In many textbooks I come across the term lowest energy. For example in atomic structures, electrons are placed in orbitals in order for the atom to have the lowest energy. But what is this energy? Potential- or kinetic energy or the sum of the two?






quantum-mechanics energy hilbert-space ground-state




quantum-mechanics energy hilbert-space ground-state






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edited 45 mins ago









Nephente

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asked 12 hours ago









ado sar

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  • 4




    The sum of the two, usually the eigenvalue of the Hamiltonian operator.
    – Lewis Miller
    11 hours ago














  • 4




    The sum of the two, usually the eigenvalue of the Hamiltonian operator.
    – Lewis Miller
    11 hours ago








4




4




The sum of the two, usually the eigenvalue of the Hamiltonian operator.
– Lewis Miller
11 hours ago




The sum of the two, usually the eigenvalue of the Hamiltonian operator.
– Lewis Miller
11 hours ago










3 Answers
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5
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The lowest energy of a quantum system is the minimum eigenvalue of the Hamiltonian of the system. The Hamiltonian is the operator which corresponds to the total energy of the system, so it is the sum of the kinetic and potential energy. This is often also referred to as the ground state energy of the system.




but what is this energy?




Heuristically, the ground state energy is the energy which the system has simply by existing. Normally, this doesn't make any sense: If I just make the system do nothing, just sit there, then it would have zero energy. We wouldn't need the fancy name.



But it turns out that this is impossible. We can never "pin down" a system and make it completely still, due to the famous Heisenberg uncertainty principle,
$$Delta x Delta p geq hbar/2.$$
The system must have some momentum, to satisfy the inequality. In turn, it will also have some energy. This is why we can never reach absolute zero! No matter how hard we try, there always remains the jiggling of the ground state.






share|cite|improve this answer





















  • Writing that it is not possible to get absolute zero because the system has to satisfy the uncertainty principle is completely wrong. Absolute zero does correspond to the minumum of energy whatever it is. It has nothing to do with energy being zero. One very good reason is that the energy is always definite within an arbitrary constant.
    – GiorgioP
    2 hours ago


















up vote
3
down vote













The sum of the two.



An electronic state like an orbital is an exact or approximate solution of some time independent Schrödinger equation, i.e. an eigenstate of the hamiltonian made by a kinetic and a potential energy term. The corresponding eigenvalue is the expectation value of such hamiltonian, evaluated on the state described by the orbital.



The expectation value of the hamiltonian can always be written as the sum of the expectation value of kinetic and potential energy. The lowest energy, is the eigenvalue of the hamiltonian with the minimum value.






share|cite|improve this answer




























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    down vote













    In QM the Schrödinger Equation gives you the solutions for the wavefunction of a particle with a given potential. Because the energy is quantized you usually find several possible values for the energy that are given by an integer number $ n $ called the Principal Quantum Number. The lowest value of $ E_n $, normally when $ n=0 $ or $ n=1 $, is the Groud-State. This means that the energy of the particle is the lowest and it is a combination of the potential energy and the kinetic energy.






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      3 Answers
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      3 Answers
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      up vote
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      The lowest energy of a quantum system is the minimum eigenvalue of the Hamiltonian of the system. The Hamiltonian is the operator which corresponds to the total energy of the system, so it is the sum of the kinetic and potential energy. This is often also referred to as the ground state energy of the system.




      but what is this energy?




      Heuristically, the ground state energy is the energy which the system has simply by existing. Normally, this doesn't make any sense: If I just make the system do nothing, just sit there, then it would have zero energy. We wouldn't need the fancy name.



      But it turns out that this is impossible. We can never "pin down" a system and make it completely still, due to the famous Heisenberg uncertainty principle,
      $$Delta x Delta p geq hbar/2.$$
      The system must have some momentum, to satisfy the inequality. In turn, it will also have some energy. This is why we can never reach absolute zero! No matter how hard we try, there always remains the jiggling of the ground state.






      share|cite|improve this answer





















      • Writing that it is not possible to get absolute zero because the system has to satisfy the uncertainty principle is completely wrong. Absolute zero does correspond to the minumum of energy whatever it is. It has nothing to do with energy being zero. One very good reason is that the energy is always definite within an arbitrary constant.
        – GiorgioP
        2 hours ago















      up vote
      5
      down vote













      The lowest energy of a quantum system is the minimum eigenvalue of the Hamiltonian of the system. The Hamiltonian is the operator which corresponds to the total energy of the system, so it is the sum of the kinetic and potential energy. This is often also referred to as the ground state energy of the system.




      but what is this energy?




      Heuristically, the ground state energy is the energy which the system has simply by existing. Normally, this doesn't make any sense: If I just make the system do nothing, just sit there, then it would have zero energy. We wouldn't need the fancy name.



      But it turns out that this is impossible. We can never "pin down" a system and make it completely still, due to the famous Heisenberg uncertainty principle,
      $$Delta x Delta p geq hbar/2.$$
      The system must have some momentum, to satisfy the inequality. In turn, it will also have some energy. This is why we can never reach absolute zero! No matter how hard we try, there always remains the jiggling of the ground state.






      share|cite|improve this answer





















      • Writing that it is not possible to get absolute zero because the system has to satisfy the uncertainty principle is completely wrong. Absolute zero does correspond to the minumum of energy whatever it is. It has nothing to do with energy being zero. One very good reason is that the energy is always definite within an arbitrary constant.
        – GiorgioP
        2 hours ago













      up vote
      5
      down vote










      up vote
      5
      down vote









      The lowest energy of a quantum system is the minimum eigenvalue of the Hamiltonian of the system. The Hamiltonian is the operator which corresponds to the total energy of the system, so it is the sum of the kinetic and potential energy. This is often also referred to as the ground state energy of the system.




      but what is this energy?




      Heuristically, the ground state energy is the energy which the system has simply by existing. Normally, this doesn't make any sense: If I just make the system do nothing, just sit there, then it would have zero energy. We wouldn't need the fancy name.



      But it turns out that this is impossible. We can never "pin down" a system and make it completely still, due to the famous Heisenberg uncertainty principle,
      $$Delta x Delta p geq hbar/2.$$
      The system must have some momentum, to satisfy the inequality. In turn, it will also have some energy. This is why we can never reach absolute zero! No matter how hard we try, there always remains the jiggling of the ground state.






      share|cite|improve this answer












      The lowest energy of a quantum system is the minimum eigenvalue of the Hamiltonian of the system. The Hamiltonian is the operator which corresponds to the total energy of the system, so it is the sum of the kinetic and potential energy. This is often also referred to as the ground state energy of the system.




      but what is this energy?




      Heuristically, the ground state energy is the energy which the system has simply by existing. Normally, this doesn't make any sense: If I just make the system do nothing, just sit there, then it would have zero energy. We wouldn't need the fancy name.



      But it turns out that this is impossible. We can never "pin down" a system and make it completely still, due to the famous Heisenberg uncertainty principle,
      $$Delta x Delta p geq hbar/2.$$
      The system must have some momentum, to satisfy the inequality. In turn, it will also have some energy. This is why we can never reach absolute zero! No matter how hard we try, there always remains the jiggling of the ground state.







      share|cite|improve this answer












      share|cite|improve this answer



      share|cite|improve this answer










      answered 10 hours ago









      Hanting Zhang

      40216




      40216












      • Writing that it is not possible to get absolute zero because the system has to satisfy the uncertainty principle is completely wrong. Absolute zero does correspond to the minumum of energy whatever it is. It has nothing to do with energy being zero. One very good reason is that the energy is always definite within an arbitrary constant.
        – GiorgioP
        2 hours ago


















      • Writing that it is not possible to get absolute zero because the system has to satisfy the uncertainty principle is completely wrong. Absolute zero does correspond to the minumum of energy whatever it is. It has nothing to do with energy being zero. One very good reason is that the energy is always definite within an arbitrary constant.
        – GiorgioP
        2 hours ago
















      Writing that it is not possible to get absolute zero because the system has to satisfy the uncertainty principle is completely wrong. Absolute zero does correspond to the minumum of energy whatever it is. It has nothing to do with energy being zero. One very good reason is that the energy is always definite within an arbitrary constant.
      – GiorgioP
      2 hours ago




      Writing that it is not possible to get absolute zero because the system has to satisfy the uncertainty principle is completely wrong. Absolute zero does correspond to the minumum of energy whatever it is. It has nothing to do with energy being zero. One very good reason is that the energy is always definite within an arbitrary constant.
      – GiorgioP
      2 hours ago










      up vote
      3
      down vote













      The sum of the two.



      An electronic state like an orbital is an exact or approximate solution of some time independent Schrödinger equation, i.e. an eigenstate of the hamiltonian made by a kinetic and a potential energy term. The corresponding eigenvalue is the expectation value of such hamiltonian, evaluated on the state described by the orbital.



      The expectation value of the hamiltonian can always be written as the sum of the expectation value of kinetic and potential energy. The lowest energy, is the eigenvalue of the hamiltonian with the minimum value.






      share|cite|improve this answer

























        up vote
        3
        down vote













        The sum of the two.



        An electronic state like an orbital is an exact or approximate solution of some time independent Schrödinger equation, i.e. an eigenstate of the hamiltonian made by a kinetic and a potential energy term. The corresponding eigenvalue is the expectation value of such hamiltonian, evaluated on the state described by the orbital.



        The expectation value of the hamiltonian can always be written as the sum of the expectation value of kinetic and potential energy. The lowest energy, is the eigenvalue of the hamiltonian with the minimum value.






        share|cite|improve this answer























          up vote
          3
          down vote










          up vote
          3
          down vote









          The sum of the two.



          An electronic state like an orbital is an exact or approximate solution of some time independent Schrödinger equation, i.e. an eigenstate of the hamiltonian made by a kinetic and a potential energy term. The corresponding eigenvalue is the expectation value of such hamiltonian, evaluated on the state described by the orbital.



          The expectation value of the hamiltonian can always be written as the sum of the expectation value of kinetic and potential energy. The lowest energy, is the eigenvalue of the hamiltonian with the minimum value.






          share|cite|improve this answer












          The sum of the two.



          An electronic state like an orbital is an exact or approximate solution of some time independent Schrödinger equation, i.e. an eigenstate of the hamiltonian made by a kinetic and a potential energy term. The corresponding eigenvalue is the expectation value of such hamiltonian, evaluated on the state described by the orbital.



          The expectation value of the hamiltonian can always be written as the sum of the expectation value of kinetic and potential energy. The lowest energy, is the eigenvalue of the hamiltonian with the minimum value.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 11 hours ago









          GiorgioP

          1,209212




          1,209212






















              up vote
              1
              down vote













              In QM the Schrödinger Equation gives you the solutions for the wavefunction of a particle with a given potential. Because the energy is quantized you usually find several possible values for the energy that are given by an integer number $ n $ called the Principal Quantum Number. The lowest value of $ E_n $, normally when $ n=0 $ or $ n=1 $, is the Groud-State. This means that the energy of the particle is the lowest and it is a combination of the potential energy and the kinetic energy.






              share|cite|improve this answer

























                up vote
                1
                down vote













                In QM the Schrödinger Equation gives you the solutions for the wavefunction of a particle with a given potential. Because the energy is quantized you usually find several possible values for the energy that are given by an integer number $ n $ called the Principal Quantum Number. The lowest value of $ E_n $, normally when $ n=0 $ or $ n=1 $, is the Groud-State. This means that the energy of the particle is the lowest and it is a combination of the potential energy and the kinetic energy.






                share|cite|improve this answer























                  up vote
                  1
                  down vote










                  up vote
                  1
                  down vote









                  In QM the Schrödinger Equation gives you the solutions for the wavefunction of a particle with a given potential. Because the energy is quantized you usually find several possible values for the energy that are given by an integer number $ n $ called the Principal Quantum Number. The lowest value of $ E_n $, normally when $ n=0 $ or $ n=1 $, is the Groud-State. This means that the energy of the particle is the lowest and it is a combination of the potential energy and the kinetic energy.






                  share|cite|improve this answer












                  In QM the Schrödinger Equation gives you the solutions for the wavefunction of a particle with a given potential. Because the energy is quantized you usually find several possible values for the energy that are given by an integer number $ n $ called the Principal Quantum Number. The lowest value of $ E_n $, normally when $ n=0 $ or $ n=1 $, is the Groud-State. This means that the energy of the particle is the lowest and it is a combination of the potential energy and the kinetic energy.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered 7 hours ago









                  Kirtpole

                  1359




                  1359






























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