Notes Two dimensional Harmonic Oscillator A two-dimensional harmonic oscillator is a physical system in which a particle is subject to forces that can be described by two independent harmonic potentials in two perpendicular directions. This …

Notes Comparison of classical and quantum probability density of harmonic oscillator The comparison between classical and quantum probability density of a harmonic oscillator highlights some fundamental differences between classical mechanics and quantum mechanics. The harmonic …

Notes Harmonic oscillator problem by matrix method Matrix Representation: Represent the Hamiltonian operator as a matrix in a finite-dimensional basis. You need to choose an appropriate basis, often involving position or momentum states, and …

Notes Discussion of the problem of one dimensional harmonic oscillator in quantum mechanics The Hamiltonian operatorH = Px²/2m + 1/2 mw²X²Px is the momentum operatorX is the position operatorWe introduce two non Hermitian operatorsIt is known thatExpression ...