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

Recommended explanations on Physics Textbooks

Famous Physicists

Modern Physics

Torque and Rotational Motion

Electricity and Magnetism

Radiation

Turning Points in Physics

Study anywhere. Anytime. Across all devices.

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 $x = L$ )?