Homework Help is Here – Start Your Trial Now!
Science
Physics
1. (QM) For a particle of mass M confined to the region << with no other forces acting on it, solutions of the time independent Schrödinger equation (T.I.S.E.) of the following form exist. (x) = B sin(mxx/b) Use the boundary conditions for this problem to find the values of m for which this this is a valid solution of the time-independent Schrödinger equation (T.I.S.E.). Show by direct substitution that this is a solution of the T.I.S.E. and, hence, derive an expression for the energy of the particle in terms of b, and m and M. Normalise this wave function. For the lowest allowed value of m, estimate the probability of observing the particle within 10% of the middle the region. The transition m+2+m for an electron trapped in a 1-dimensional potential 2nm across produces light with a wavelength of 823 nm. What is the value of m for this transition?

1. (QM) For a particle of mass M confined to the region << with no other forces acting on it, solutions of the time independent Schrödinger equation (T.I.S.E.) of the following form exist. (x) = B sin(mxx/b) Use the boundary conditions for this problem to find the values of m for which this this is a valid solution of the time-independent Schrödinger equation (T.I.S.E.). Show by direct substitution that this is a solution of the T.I.S.E. and, hence, derive an expression for the energy of the particle in terms of b, and m and M. Normalise this wave function. For the lowest allowed value of m, estimate the probability of observing the particle within 10% of the middle the region. The transition m+2+m for an electron trapped in a 1-dimensional potential 2nm across produces light with a wavelength of 823 nm. What is the value of m for this transition?

University Physics Volume 3
University Physics Volume 3
17th Edition
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:William Moebs, Jeff Sanny
Chapter7: Quantum Mechanics
Section: Chapter Questions
Problem 12CQ: Explain the difference between time-dependent and independent SchrÖdinger's equations.
See similar textbooks
icon
Related questions
Question

please help me with this question

1. (QM) For a particle of mass M confined to the region << with no other forces acting on it, solutions of the time independent Schrödinger equation (T.I.S.E.) of the following form exist. (x) = B sin(mxx/b) Use the boundary conditions for this problem to find the values of m for which this this is a valid solution of the time-independent Schrödinger equation (T.I.S.E.). Show by direct substitution that this is a solution of the T.I.S.E. and, hence, derive an expression for the energy of the particle in terms of b, and m and M. Normalise this wave function. For the lowest allowed value of m, estimate the probability of observing the particle within 10% of the middle the region. The transition m+2+m for an electron trapped in a 1-dimensional potential 2nm across produces light with a wavelength of 823 nm. What is the value of m for this transition?
Transcribed Image Text:1. (QM) For a particle of mass M confined to the region << with no other forces acting on it, solutions of the time independent Schrödinger equation (T.I.S.E.) of the following form exist. (x) = B sin(mxx/b) Use the boundary conditions for this problem to find the values of m for which this this is a valid solution of the time-independent Schrödinger equation (T.I.S.E.). Show by direct substitution that this is a solution of the T.I.S.E. and, hence, derive an expression for the energy of the particle in terms of b, and m and M. Normalise this wave function. For the lowest allowed value of m, estimate the probability of observing the particle within 10% of the middle the region. The transition m+2+m for an electron trapped in a 1-dimensional potential 2nm across produces light with a wavelength of 823 nm. What is the value of m for this transition?
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
University Physics Volume 3
University Physics Volume 3
Physics
ISBN:
9781938168185
Author:
William Moebs, Jeff Sanny
Publisher:
OpenStax
Classical Dynamics of Particles and Systems
Classical Dynamics of Particles and Systems
Physics
ISBN:
9780534408961
Author:
Stephen T. Thornton, Jerry B. Marion
Publisher:
Cengage Learning
Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
Physics
ISBN:
9781133104261
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Modern Physics
Modern Physics
Physics
ISBN:
9781111794378
Author:
Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:
Cengage Learning
Glencoe Physics: Principles and Problems, Student…
Glencoe Physics: Principles and Problems, Student…
Physics
ISBN:
9780078807213
Author:
Paul W. Zitzewitz
Publisher:
Glencoe/McGraw-Hill
Physics for Scientists and Engineers: Foundations…
Physics for Scientists and Engineers: Foundations…
Physics
ISBN:
9781133939146
Author:
Katz, Debora M.
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS