What is lowest energy?
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In many textbook i come up with the term of lowest energy. For example in atomic structures electrons are placed in orbitals in order the atom to have the lowest energy? but what is this energy? potential or kinetic or the sum of the two?
quantum-mechanics energy hilbert-space ground-state
edited 5 hours ago
Qmechanic♦
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asked 5 hours ago
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In many textbook i come up with the term of lowest energy. For example in atomic structures electrons are placed in orbitals in order the atom to have the lowest energy? but what is this energy? potential or kinetic or the sum of the two?
quantum-mechanics energy hilbert-space ground-state
edited 5 hours ago
Qmechanic♦
100k121821135
asked 5 hours ago
ado sar
1288
3
The sum of the two, usually the eigenvalue of the Hamiltonian operator.
– Lewis Miller
5 hours ago
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
In many textbook i come up with the term of lowest energy. For example in atomic structures electrons are placed in orbitals in order the atom to have the lowest energy? but what is this energy? potential or kinetic or the sum of the two?
quantum-mechanics energy hilbert-space ground-state
edited 5 hours ago
Qmechanic♦
100k121821135
asked 5 hours ago
ado sar
1288
In many textbook i come up with the term of lowest energy. For example in atomic structures electrons are placed in orbitals in order the atom to have the lowest energy? but what is this energy? potential or kinetic or the sum of the two?
quantum-mechanics energy hilbert-space ground-state
quantum-mechanics energy hilbert-space ground-state
edited 5 hours ago
Qmechanic♦
100k121821135
asked 5 hours ago
ado sar
1288
edited 5 hours ago
Qmechanic♦
100k121821135
asked 5 hours ago
ado sar
1288
edited 5 hours ago
Qmechanic♦
100k121821135
edited 5 hours ago
Qmechanic♦
100k121821135
edited 5 hours ago
Qmechanic♦
100k121821135
100k121821135
asked 5 hours ago
ado sar
1288
asked 5 hours ago
ado sar
1288
asked 5 hours ago
ado sar
1288
1288
3
The sum of the two, usually the eigenvalue of the Hamiltonian operator.
– Lewis Miller
5 hours ago
add a comment |
3
The sum of the two, usually the eigenvalue of the Hamiltonian operator.
– Lewis Miller
5 hours ago
3
3
The sum of the two, usually the eigenvalue of the Hamiltonian operator.
– Lewis Miller
5 hours ago
The sum of the two, usually the eigenvalue of the Hamiltonian operator.
– Lewis Miller
5 hours ago
add a comment |
3 Answers
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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.
answered 5 hours ago
GiorgioP
1,199212
add a comment |
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2
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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.
answered 4 hours ago
Hanting Zhang
37216
add a comment |
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.
answered 43 mins ago
Kirtpole
1358
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
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.
answered 5 hours ago
GiorgioP
1,199212
add a comment |
up vote
2
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.
answered 5 hours ago
GiorgioP
1,199212
add a comment |
up vote
2
down vote
up vote
2
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.
answered 5 hours ago
GiorgioP
1,199212
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.
answered 5 hours ago
GiorgioP
1,199212
answered 5 hours ago
GiorgioP
1,199212
answered 5 hours ago
GiorgioP
1,199212
answered 5 hours ago
GiorgioP
1,199212
1,199212
add a comment |
add a comment |
up vote
2
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.
answered 4 hours ago
Hanting Zhang
37216
add a comment |
up vote
2
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.
answered 4 hours ago
Hanting Zhang
37216
add a comment |
up vote
2
down vote
up vote
2
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.
answered 4 hours ago
Hanting Zhang
37216
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.
answered 4 hours ago
Hanting Zhang
37216
answered 4 hours ago
Hanting Zhang
37216
answered 4 hours ago
Hanting Zhang
37216
answered 4 hours ago
Hanting Zhang
37216
37216
add a comment |
add a comment |
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.
answered 43 mins ago
Kirtpole
1358
add a comment |
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.
answered 43 mins ago
Kirtpole
1358
add a comment |
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.
answered 43 mins ago
Kirtpole
1358
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.
answered 43 mins ago
Kirtpole
1358
answered 43 mins ago
Kirtpole
1358
answered 43 mins ago
Kirtpole
1358
answered 43 mins ago
Kirtpole
1358
1358
add a comment |
add a comment |
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The sum of the two, usually the eigenvalue of the Hamiltonian operator.
– Lewis Miller
5 hours ago