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
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![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](/uploads/image/z/9850138-34-8.jpg?t=%E9%97%AE%E4%B8%80%E9%81%93%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%A6%E7%9A%84%E9%A2%98Consider+a+particle+of+mass+in+the+state+%7Cn%3E+of+a+box+of+length+L.Find+the+force+F%3D-dE%2FdL%EF%BC%88%E5%81%8F%E5%BE%AE%E5%88%86%2C%E9%82%A3%E4%B8%AA%E7%AC%A6%E5%8F%B7%E6%89%93%E4%B8%8D%E5%87%BA%E6%9D%A5%E7%94%A8d%E4%BB%A3%E6%9B%BF%E4%BA%86%EF%BC%89encountered+when+the+walls+are+slowly+pushed+in+%2Cassuming+the+particle+remains+in)
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
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.
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
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)
粒子与势垒碰撞后以相同的速度反弹回去,所以与一个势垒两次碰撞的间隔是
t=2L/v=2L/(根号下2En/m)
则碰撞频率是
f=1/t=根号下(2En/m)/2L
在一次碰撞中改变的动量是2p,所以单位时间内动量改变量即F是
F=2pf=2根号下(2mEn)*根号下(2En/m)/2L=2En/L
和前面的结果是相同的.