OurBigBook.com $£ Sponsor €¥ 中国独裁统治 China Dictatorship 新疆改造中心、六四事件、法轮功、郝海东、709大抓捕、2015巴拿马文件邓家贵、低端人口、西藏骚乱

Quantum harmonic oscillator

This equation is a subcase of Equation 13. "Schrödinger equation for a one dimensional particle" with

V (x) = x^{2}

.

We get the time-independent Schrödinger equation by substituting this

V

into Equation 14. "time-independent Schrödinger equation for a one dimensional particle":

[- \frac{ℏ}{2 m} \frac{\partial ^{2}}{\partial x} + x^{2}] ψ = E ψ (x)

Now, there are two ways to go about this.

The first is the stupid "here's a guess" + "hey this family of solutions forms a complete bases"! This is exactly how we solved the problem at Section "Solving partial differential equations with the Fourier series", except that now the complete basis are the Hermite functions.

The second is the much celebrated ladder operator method.

Table of contents 168 4

 Ancestors

 Incoming links