問一道量子力學(xué)的題
問一道量子力學(xué)的題
Consider a particle of mass in the state |n> of a box of length L.Find the force F=-dE/dL（偏微分,那個符號打不出來用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.
Consider a particle of mass in the state |n> of a box of length L.Find the force F=-dE/dL（偏微分,那個符號打不出來用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.
英語人氣：778 ℃時間：2020-03-28 00:51:27
優(yōu)質(zhì)解答
粒子的初始能量是En=h^2n^2/(8mL^2)因為勢壘是緩慢移動的,所以滿足絕熱近似條件,因此粒子仍處于該本征態(tài)上,所以F=-dE/dL=h^2n^2/(4mL^3)=2En/L考慮經(jīng)典粒子因為En=mv^2/2所以v=根號下(2En/m)p=mv=根號下(2mEn)粒子與...
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