Friday, September 11, 2015

hilbert space - Conceptual understanding of the Quantum Harmonic oscillator


First: When we consider a quantum particle in a harmonic (quadratic) potential we say that this particle is a harmonic oscillator, because it behaves like one. Is this correct?


Now let us assume our particle is in the groundstate ψ0. This would mean that in this picture it would be described by the lowest wave with energy E0.


I have a bit of a hard time to understand what happens when we increase the energy of said particle. The old wave function disappears and we find our particle in a new state ψn with some new energy En described by a new wave in the picture. Is that correct?


Honestly, I'm giving a presentation on this topic soon, and want to visualize such a 'jump' from a lower energy state to a higher energy state of a particle in the harmonic potential, in the correct way.



Any help is greatly appreciated!




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