Eigenstates of the quantum harmonic oscillator
What do the energy eigenstates of the quantum harmonic oscillator look like?
📝 Problems+solutions:
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📚 The eigenfunctions of the quantum harmonic oscillator are famously given by the product of a polynomial and a Gaussian. In this video, we derive their mathematical form and visualize a few representative states.
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⏮️ BACKGROUND
Harmonic oscillator: • The quantum harmonic oscillator
Ladder and number operators: • Ladder and number operators of the quantum...
Eigenvalues of the quantum harmonic oscillator: • Eigenvalues of the quantum harmonic oscill...
Harmonic oscillator eigenvalues: • Eigenvalues of the quantum harmonic oscill...
The parity operator: • The parity operator in quantum mechanics
Even and odd operators: • Even and odd operators in quantum mechanics
Wave functions: • Wave functions in quantum mechanics
Position and momentum: • Position and momentum operators acting on ...
⏭️ WHAT NEXT?
Hermite polynomials: • Hermite polynomials and the quantum harmon...
Coherent states: • Coherent states in quantum mechanics
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Director and writer: BM
Producer and designer: MC