Hydrogen atom ground state with zero orbital angular moment question.

In summary, the conversation discusses the symmetry of the ground state wavefunction in the Schrodinger equation and how it relates to the expectation value of orbital angular momentum. The group also considers whether this symmetry can be determined solely based on physical concepts or if mathematical calculations are necessary. The concept of parity and its relation to spherical symmetry is also discussed.
  • #1
xfshi2000
31
0
Hi all:
As we know, if we solve the schrodinger equation, the ground state wavefunction is independent of theta and psi. We find the expectation value of ground state orbital angular momentum is zero. But if we don't do any mathematical calculation, can we conlude that?
For example, Due to symmetry of coulomb potential, Hydrogen atom (one proton plus one electron) wavefunction must be symmetric or antisymmetric (for ground state, there is no degeneracy). Then I am stuck. How can I conclude that only by virtue of physical concept or symmetry? Does symmetry means spherical symmetry?
thanks

xf
 
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  • #2
well symmetric with respect to partiy : spatial inversion. C.f with particle in box solutions.
 
  • #3
malawi_glenn said:
well symmetric with respect to partiy : spatial inversion. C.f with particle in box solutions.

Thank you. What is C.f? parity property only determines psi(-x)=+/-psi(x). where x is vector. It doesn't mean it is spherical symmetry. Could you explain more? thanks
 
  • #4
c.f means "compare with"

No, the wavefunctions just need to have positive or negative parity eigenvalue. I don't think there is a theorem which states that the symmetry of the ground state wave function must have the same symmetry as the potential.
 

Related to Hydrogen atom ground state with zero orbital angular moment question.

1. What is the ground state of a hydrogen atom with zero orbital angular momentum?

The ground state of a hydrogen atom with zero orbital angular momentum is the state in which the electron is in its lowest energy level, known as the 1s orbital. This means that the electron is closest to the nucleus and has the lowest possible energy.

2. How is the ground state of a hydrogen atom with zero orbital angular momentum determined?

The ground state of a hydrogen atom with zero orbital angular momentum is determined by solving the Schrödinger equation for the hydrogen atom. This equation takes into account the attractive force between the electron and the nucleus, as well as the electron's kinetic energy.

3. What is the significance of zero orbital angular momentum in the ground state of a hydrogen atom?

The fact that the hydrogen atom has zero orbital angular momentum in its ground state is significant because it means that the electron has a stable and well-defined position around the nucleus. This also allows for the accurate calculation of the atom's energy and other properties.

4. Can the ground state of a hydrogen atom with zero orbital angular momentum change?

Yes, the ground state of a hydrogen atom with zero orbital angular momentum can change if it absorbs or emits energy. This can cause the electron to move to a higher or lower energy level, resulting in a different ground state for the atom.

5. How does the ground state of a hydrogen atom with zero orbital angular momentum differ from other states?

The ground state of a hydrogen atom with zero orbital angular momentum is the most stable and lowest energy state for the atom. Other states, such as excited states, have higher energy levels and are less stable. The ground state also has a specific energy and electron configuration, while other states have different energies and configurations.

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