Ground State of Quantum System: l=0?

In summary, the ground state of a quantum system is generally characterized by the lowest quantum numbers, including l=0 for systems governed by a radial potential. This is also true for the finite, 3-D potential well, as implied by Griffiths in one of his problems.
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lion8172
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ground states

Homework Statement



Is it generally true that the ground state of a given quantum system corresponds to the lowest quantum numbers? For instance, is it generally true that the ground state of a system governed by a radial potential always corresponds to l=0? If not, how do we know, in particular, that the ground state of the finite, 3-D potential well corresponds to l=0? Griffiths seems to implicitly assume this fact in one of his problems (4.9): "Find the ground state (of the 3-D finite spherical well) by solving the radial equation with l=0."

Homework Equations





The Attempt at a Solution

 
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  • #2
Here is a hint, [itex] l = 0 [/itex] corresponds to a spherical configuration, which is usually the lowest eneergy state.
 

1. What is the ground state of a quantum system with angular momentum l=0?

The ground state of a quantum system with angular momentum l=0 is the lowest possible energy state of the system. In other words, it is the most stable and least energetic state that the system can exist in.

2. How is the ground state of a quantum system with l=0 determined?

The ground state of a quantum system with l=0 is determined by solving the Schrödinger equation for the system. This equation describes the behavior of quantum systems and provides information about the energy levels and wavefunctions of the system.

3. Is the ground state of a quantum system with l=0 unique?

Yes, the ground state of a quantum system with l=0 is unique. This is because the l=0 state is the lowest possible energy state for a system with no angular momentum, and there can only be one lowest energy state.

4. How does the ground state of a quantum system with l=0 differ from other energy states?

The ground state of a quantum system with l=0 has the lowest energy compared to other energy states for the same system. This means that it is the most stable and least energetic state that the system can exist in. Other energy states have higher energies and correspond to higher energy levels.

5. Can the ground state of a quantum system with l=0 change?

Yes, the ground state of a quantum system with l=0 can change if there is a change in the system's parameters or external influences. For example, if the system gains or loses energy, the ground state may shift to a different energy level. However, the l=0 state will always remain the lowest possible energy state for the system.

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