(a)
The value of
(a)
Answer to Problem 51P
The value of
Explanation of Solution
Given:
The one-dimensional box region is
The particle is in the nth state.
The wave functionis
Formula used:
The expression for
The expression for
The integral formula,
The integral formula,
Calculation:
Let,
By differentiating both sides,
The limit is
The
Solving further as,
The
Solving further as,
Conclusion:
Therefore, the value of
(b)
The comparison of
(b)
Answer to Problem 51P
The value of
Explanation of Solution
Calculation:
The value of
The value of
Which is same as in case of problem
Conclusion:
Therefore, the value of
Want to see more full solutions like this?
Chapter 34 Solutions
Physics For Scientists And Engineers Student Solutions Manual, Vol. 1
- Show that the two lowest energy states of the simple harmonic oscillator, 0(x) and 1(x) from Equation 7.57, satisfy Equation 7.55. n(x)=Nne2x2/2Hn(x),n=0,1,2,3,.... h2md2(x)dx2+12m2x2(x)=E(x).arrow_forwardCan we simultaneously measure position and energy of a quantum oscillator? Why? Why not?arrow_forwardIs it possible that when we measure the energy of a quantum particle in a box, the measurement may return a smaller value than the ground state energy? What is the highest value of the energy that we can measure for this particle?arrow_forward
- What is the maximum kinetic energy of an electron such that a collision between the electron and a stationary hydrogen atom in its ground state is definitely elastic?arrow_forwardIf the ground state energy of a simple harmonic oscillator is 1.25 eV, what is the frequency of its motion?arrow_forwardWhich one of the following functions, and why, qualifies to be a wave function of a particle that can move along the entire real axis? (x)=Aex2; (x)=Aex; (x)=Atanx; (x)=A(sinx)/x; (x)=Ae|x|arrow_forward
- If a classical harmonic oscillator can at rest, why can the quantum harmonic oscillator never be at rest? Does this violate Bohr 's correspondence principle?arrow_forwardA particle with mass m is described by the following wave function: (x)=Acoskx+Bsinkx, where A, B, and k are constants. Assuming that the particle is free, show that this function is the solution of the stationary SchrÖdinger equation for this particle and find the energy that the particle has in this state.arrow_forward
- University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStaxModern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning