Quantum-Mechanical Harmonic Oscillator

Carl W David

The classical harmonic oscillator and an elementary discussion of the quantum mechanical solutions for the harmonic oscillator are discussed.

Shu Hotta

Rinto Agustino, Saiman Saiman

Abstract. Have been calculated harmonics oscillator with Hilbert Space review. Study of harmonics oscillator in classical mechanics usually uses Newtonian and Lagrange mechanicswhile in quantum mechanics using Hamiltonian. Keywords: Hilbert Space, harmonics oscillator

Shu Hotta

Erich W. Schmid, Gerhard Spitz, Wolfgang Lösch

<p>Sihui Yan¹, Jie Huang²</p>

Quantum mechanics holds a very important position as the theoretical foundation of the micro world. Harmonic oscillator system is a very classical model in quantum mechanics. In this paper, the wave function of a three-dimensional linear harmonic oscillator is derived based on the linear harmonic oscillator model in quantum mechanics. According to the probabilistic interpretation of quantum mechanics, we obtain the probability density function of the harmonic oscillator electron cloud. In this paper, Monte Carlo selection method is used for sampling, and Mathematica software is used to draw electron cloud images with different quantum number, so that people can intuitively see the distribution of electron cloud in three-dimensional space.