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

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The term "non-degenerate spectrum of bound states" in quantum mechanics (QM) refers to the condition where no two bound states possess the same energy level. This concept is crucial for understanding the unique energy states of a quantum system. Additionally, the time-independent Schrödinger equation exhibits reflection invariance, meaning that the solutions remain unchanged under the transformation of coordinates from x to -x, which also applies to the time coordinate.

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  • Basic understanding of quantum mechanics principles
  • Familiarity with the time-independent Schrödinger equation
  • Knowledge of energy states and degeneracy in quantum systems
  • Concept of reflection invariance in physics
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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 Schrödinger eqn reflection invariant? (I'm not sure I quite know what that means either...)

Thanks!
 
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"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.)
 
Thanks, alxm!
 

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