Chapter 6: Q15DQ (page 1353)

A particle is confined to a finite potential well in the region 0 < x < L . How does the area under the graph of $| ψ |^{2}$ in the region 0 < x < L compare to the total area under the graph of $| ψ |^{2}$ when including all possible x?

Short Answer

Expert verified

The area under the graph of ${|ψ|}^{2}$ in the region 0 < x < L constitutes the majority of the total area under the graph of ${|ψ|}^{2}$ when including all possible x.

Step by step solution

Wave function of a particle in finite potential

The wave function of particle in finite potential is sinusoidal in the region 0<x<L of finite potential well and it is exponential outside region 0<x<L the finite potential well.

Comparison of the total area of |ψ|2 under and outside the region 0<x<L

The rate of decay of falling exponential part of wave function outside the region 0<x<L is very large therefore the area under the graph of ${|ψ|}^{2}$ is practically zero.

Hence, the majority of the total area lies under the graph ${|ψ|}^{2}$ in region 0<x<L of finite potential well.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

A particle is confined to a finite potential well in the region 0 < x < L . How does the area under the graph of $| ψ |^{2}$ in the region 0 < x < L compare to the total area under the graph of $| ψ |^{2}$ when including all possible x?

Short Answer

Step by step solution

Wave function of a particle in finite potential

Comparison of the total area of |ψ|2 under and outside the region 0<x<L

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Particle Model of Matter

Fields in Physics

Radiation

Mechanics and Materials

Classical Mechanics

Rotational Dynamics

Study anywhere. Anytime. Across all devices.

A particle is confined to a finite potential well in the region 0 < x < L . How does the area under the graph of |ψ|2 in the region 0 < x < L compare to the total area under the graph of |ψ|2 when including all possible x?

Short Answer

Step by step solution

Wave function of a particle in finite potential

Comparison of the total area of |ψ|2 under and outside the region 0<x<L

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Particle Model of Matter

Fields in Physics

Radiation

Mechanics and Materials

Classical Mechanics

Rotational Dynamics

Study anywhere. Anytime. Across all devices.

A particle is confined to a finite potential well in the region 0 < x < L . How does the area under the graph of $| ψ |^{2}$ in the region 0 < x < L compare to the total area under the graph of $| ψ |^{2}$ when including all possible x?