QM Newbie: What Does 'Non-Degenerate Spectrum of Boundstates' Mean?

In summary, the conversation discusses the concept of "degenerate" energy states and the meaning of "the spectrum of bound states is non-degenerate". It also explores the reflection invariance of the time-independent Schrodinger equation and how it affects the solutions.
  • #1
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Hi, I am new to QM, so advanced apologies for the dumb questions to follow. What does "the spectrum of boundstates is non-degenerate" mean? And why is the time-independent Schrodinger eqn reflection invariant? (I'm not sure I quite know what that means either...)

Thanks!
 
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  • #2
"Degenerate" energy states are ones which have the same energy. So "the spectrum of bound states is non-degenerate" means no two bound states have the same energy.
(This is specific to your system though, and not true in general)
A reflection is a transformation of coordinates x -> -x. So it means that the equation gives the same solutions if you invert the coordinate system.
(which may also include the _time_ coordinate, since it's time-independent, changing the sign of the time coordinate will by definition not change anything.)
 
  • #3
Thanks, alxm!
 

1. What is a non-degenerate spectrum in quantum mechanics?

In quantum mechanics, a non-degenerate spectrum refers to a set of energy levels that are all distinct and do not overlap. This means that each energy level corresponds to a unique quantum state and there are no degenerate states with the same energy level.

2. What are bound states in quantum mechanics?

Bound states in quantum mechanics are states in which a particle is confined within a potential well or barrier. These states have discrete energy levels and the particle cannot escape from the potential well without gaining energy.

3. How is the non-degenerate spectrum of bound states different from a degenerate spectrum?

A degenerate spectrum in quantum mechanics refers to a set of energy levels that are not distinct and can overlap. This means that there are multiple quantum states with the same energy level. In contrast, a non-degenerate spectrum has distinct energy levels with no overlap.

4. What is the significance of a non-degenerate spectrum of bound states?

A non-degenerate spectrum of bound states has important implications in quantum mechanics. It allows for a clear distinction between different energy levels and quantum states, making it easier to study and understand the behavior of particles in a potential well. It also plays a crucial role in the development of quantum technologies.

5. Can a non-degenerate spectrum of bound states exist in all systems?

No, a non-degenerate spectrum of bound states is only possible in systems with a finite number of energy levels, such as a particle in a potential well. In systems with infinite energy levels, such as a free particle, the spectrum will always be degenerate.

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