On Tuesday we will start a new topic: quantum mechanics in two-dimensions. Things change as we go from 1D to 2 or 3 dimensions. Degeneracy is a big part of that. There is degeneracy in the 2D harmonic oscillator and in the hydrogen atom. Energy eigenstate degeneracy is critical to the phenomenology of our world, including semiconductors, biology, chemistry etc.
On Tuesday will will talk about the 2D harmonic oscillator. Much of what we will learn will help pave the way for understanding the hydrogen atom a bit later this quarter.
Added: also \(E_2= 2 \hbar \omega\), \(E_3= 3 \hbar \omega\) ... (see list in picture below)
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