题目

问一道量子力学的题
Consider a particle of mass in the state |n> of a box of length L.Find the force F=-dE/dL（偏微分,那个符号打不出来用d代替了）encountered when the walls are slowly pushed in ,assuming the particle remains in the nth state of the box as its size changes.Consider a classical particle of energy En in this box.Find its velocity,the frequency of collision on a given wall,the momentum transfer per collision,and hence the average force.Compare it to -dE/dL computed above.

提问时间：2020-07-27

答案

粒子的初始能量是En=h^2n^2/(8mL^2)因为势垒是缓慢移动的,所以满足绝热近似条件,因此粒子仍处于该本征态上,所以F=-dE/dL=h^2n^2/(4mL^3)=2En/L考虑经典粒子因为En=mv^2/2所以v=根号下(2En/m)p=mv=根号下(2mEn)粒子与...