Chapter 40: Q. 36 (page 1176)

For a particle in a finite potential well of width L and depth $U_{0}$ , what is the ratio of the probability Prob ( in $δx$ at $x = L + η$ ) to the probability Prob ( in $δx$ at $x = L$ )?

Short Answer

Expert verified

The probability ratio will be $0.135 .$

Step by step solution

Given information

We have given,

Length of potential well =L

Depth = $U_{0}$

We have to find the ratio of probability of the system.

Simplify

We know that the probability of any system is describe by

$P = \int {|φ (x)|}^{2} δx$

Where $φ (x)$ is eigenstate of the system.

Then the ration will be found out as

$ratio = \frac{Probability at x = L + η}{Probability at x = L} ratio = \frac{\int {|φ (L + η)|}^{2} δx}{\int {|φ (L)|}^{2} δx} ratio = \frac{{|φ (L + η)|}^{2}}{{|φ (L)|}^{2}}$

Since, we can use here the probability of parodic wave function. Then the wave function at the $L + η$ will be

$φ (L + η) = φ (L) e^{- (x - L) / η}$

then,

$ratio = e^{- 2} = 0.135$

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For a particle in a finite potential well of width L and depth $U_{0}$ , what is the ratio of the probability Prob ( in $δx$ at $x = L + η$ ) to the probability Prob ( in $δx$ at $x = L$ )?

Short Answer

Step by step solution

Given information

Simplify

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For a particle in a finite potential well of width L and depthU0 , what is the ratio of the probability Prob ( in δxat x=L+η) to the probability Prob ( in δx atx=L)?

Short Answer

Step by step solution

Given information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

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For a particle in a finite potential well of width L and depth $U_{0}$ , what is the ratio of the probability Prob ( in $δx$ at $x = L + η$ ) to the probability Prob ( in $δx$ at $x = L$ )?