Logo
Home Study Material Contact Search
AI Chat FREE
  1. sciences
  2. physics
  3. consider a particle of mass m that can move in a o

Consider a particle of mass m that can move in a one-dimensional box of size L...

60.1K

Verified Solution

Question

Physics

Consider a particle of mass m that can move in a one-dimensionalbox of size L with the edges of the box at x=0 and x = L. Thepotential is zero inside the box and infinite outside.

You may need the following integrals:

∫ 0 1 d y sin ⁡ ( n π y ) 2 = 1 / 2 ,  for allinteger  n

∫ 0 1 d y sin ⁡ ( n π y ) 2 y = 1 / 4 ,  for allinteger  n

∫ 0 1 d y sin ⁡ ( n π y ) 2 y 2 = 1 6 − 1 16 π 2,  for all integer  n

(a) Write down the time-independent Schrodingerequation describing the system, and determine whether ψ = sin ⁡ ( 2π x / L )is an energy eigenstate by checking whether it satisfiesthe Schrodinger equation. If it is an energy eigenstate, what isthe energy? [10 pts]

(b) Suppose we measure the position of theparticle in the state in part (a) repeatedly and average theresults. Determine the result. [10 pts]

(c) What are the most likely places to find theparticle in a single measurement if it is in the state in part (a)?[10 pts]

Answer & Explanation Solved by verified expert
4.4 Ratings (778 Votes)
    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Zin AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Q

You are given that cos(A)=-7/25, with A in Quadrant lll and cos(B)=3/5, with B in Quadrant...

Basic Math
Q

A generic brand of all-purpose fertilizer G claims to contain 10 percent phosphorous, a nutrient which...

Statistics
Q

Gilbert Moss and Angela Pasaic spent several summers during their college years working at archaeological sites...

Operations Management
Q

how do you find the equivalent positions for a monoclinic space group for example a C2/m...

Chemistry
Q

Lazer Technologies Inc. (LTI) has produced a total of 20 high-power laser systems that could be...

Basic Math
Q

A small town has two local high schools. High School A currently has 900 students...

Basic Math
Q

Please read over the following scenario Then choose an answer that best describes why the...

Statistics
Q

The probability distribution of X the number of imperfections per 10 meters of a synthetic...

Statistics
Q

A projectile is fired with an initial speed of 220 m s and angle of...

Calculus
Q

A company uses a periodic inventory system. On August 1, the company had 6 items...

Accounting
Q

If the preferred dividend is US $50 and the required rate of return is 2.5%,...

Accounting
Q

The last step in the preparation of the master budget is the budgeted income statement....

Accounting