Hamiltonian and energy eigenstates
The Hamiltonian of the particle is:
The time-independent Schrödinger equation (TISE) is, $${\displaystyle {\hat {H}}\left|\psi \right\rangle =E\left|\psi \right\rangle ~,}$$ 展开

• Quantum pendulum
• Quantum machine – human-made device whose collective motion follows the laws of quantum mechanics
• Gas in a harmonic trap – Quantum mechanical model 展开

• Quantum Harmonic Oscillator
• Rationale for choosing the ladder operators
• Live 3D intensity plots of quantum harmonic oscillator Archived 12 July 2011 at the Wayback Machine 展开

The one-dimensional harmonic oscillator is readily generalizable to N dimensions, where N = 1, 2, 3, …. In one dimension, the position of the particle was specified by a single 展开

Harmonic oscillators lattice: phonons
The notation of a harmonic oscillator can be extended to a one-dimensional lattice of many particles. … 展开

• Griffiths, David J. (2004). Introduction to Quantum Mechanics (2nd ed.). Prentice Hall. ISBN 978-0-13-805326-0.
• Liboff, … 展开