Summary of Quantum and Statistical Mechanics

Abstract

In Quantum Mechanics, the state of a particle in one dimension and in presence of a potential U(x,t), is entirely described by a complex wave function ψ(x,t) obeying the time dependent Schrödinger equation

$$i\hbar \frac{{\partial \psi \left( {x,t} \right)}}{{\partial t}} = - \frac{{{\hbar ^2}}}{{2m}}\frac{{{\partial ^2}\psi \left( {x,t} \right)}}{{\partial {x^2}}} + U\left( {x,t} \right)\psi \left( {x,t} \right)$$

where m is the mass of the particle and ħ is the Planck constant, h, divided by 2π.