Answer to Question #189029 in Quantum Mechanics for yash

Question #189029

A particle trapped in a one-dimensional box of length L is described by the wave function ψ = ax. What is the probability that the particle is lying between L1 and L2?


1
Expert's answer
2021-05-05T10:55:18-0400

By definition, the probability that the particle is lying between L1 and L2 is given as follows (see http://www.iitg.ac.in/asil/QM-02.pdf):


P=L1L2ψ2dxP = \int_{L_1}^{L_2}|\psi|^2dx

where


ψ2=(ax)2=a2x2|\psi|^2 = (ax)^2 =a^2x^2

is the modulus of the wavefunction. Thus, evaluating the integral, obtain:


P=a2L1L2x2dx=a2x33L1L2=a23(L23L13)P = a^2\int_{L_1}^{L_2}x^2dx = a^2\left.\dfrac{x^3}{3}\right |_{L_1}^{L_2} = \dfrac{a^2}{3}(L_2^3-L_1^3)

Answer. P=a23(L23L13)P = \dfrac{a^2}{3}(L_2^3-L_1^3).


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment