神马作文网一道量子力学的证明题一道证明题A particle is in the ground state of a box of
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一道量子力学的证明题
一道证明题
A particle is in the ground state of a box of length L.
Suddenly the box expands(symmetrically) to twice its size,leaving the wave function undisturbed.
Show that the probability of finding the particle in the ground state of the new box is (8/3π)^2(平方)
请问这个怎么证明,
一道证明题
A particle is in the ground state of a box of length L.
Suddenly the box expands(symmetrically) to twice its size,leaving the wave function undisturbed.
Show that the probability of finding the particle in the ground state of the new box is (8/3π)^2(平方)
请问这个怎么证明,
粒子原来的波函数是
phi1=根号(2/L)sin(pi*x/L)
盒子扩大后粒子的基态波函数是
phi2=根号(1/L)sin(pi*x/2L+pi/4) (注意由于盒子是均匀扩大的,扩大后势阱中心在x=L/2而不是x=L处,所以要向左平移L/2)
扩大后粒子处于基态和其他激发态的叠加态,且基态的系数是
a=∫phi1*phi2dx 积分限是0到L
=8/3pi
所以在扩大后的盒子里测得粒子处于基态的概率是
|a|^2
=(8/3pi)^2
phi1=根号(2/L)sin(pi*x/L)
盒子扩大后粒子的基态波函数是
phi2=根号(1/L)sin(pi*x/2L+pi/4) (注意由于盒子是均匀扩大的,扩大后势阱中心在x=L/2而不是x=L处,所以要向左平移L/2)
扩大后粒子处于基态和其他激发态的叠加态,且基态的系数是
a=∫phi1*phi2dx 积分限是0到L
=8/3pi
所以在扩大后的盒子里测得粒子处于基态的概率是
|a|^2
=(8/3pi)^2
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