Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
expand_more
expand_more
format_list_bulleted
Question
Chapter 8, Problem 8.29P
(a)
To determine
Prove that if a potential well consists of one bound state, any deeper of wider well also consists of minimum one bound state.
(b)
To determine
Verify the corollary that every potential well in one-dimension posses a bound state.
(c)
To determine
Check whether the theory and corollary mentioned in part (b) may extend to 2 and 3 dimensions.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Find the wave function and energy for the infinite-walled well problemCould you explain it to me step by step and in detail?Thanks a lot
Find the Dual of the function below and check if it is self-dual:F4 = (XY + YZ + ZX)
Calculate the expectation value of x2 in the state described by ψ = e -bx, where b is a ħ constant. In this system x ranges from 0 to ∞.
Chapter 8 Solutions
Introduction To Quantum Mechanics
Knowledge Booster
Similar questions
- The wavefunction of is Ψ(x) = Axe(−ax^2)/2 for with energy E = 3aℏ2/2m. Find the bounding potential V(x). Looking at the potential’s form, can you write down the two energy levels that are immediately above E?arrow_forwardNormalize the wave function Ψ (x) = A exp (–ax2), A and a are constants, over the domain −∞ ≤ x ≤ ∞arrow_forwardObtain the value of the Lagrange multiplier for the particle above the bowl given by x^2+y^2=azarrow_forward
- The wavefunction of is Ψ(x) = Axe−αx2/2 for with energy E = 3αℏ2/2m. Find the bounding potential V(x). Looking at the potential’s form, can you write down the two energy levels that are immediately above ??arrow_forwardAt what displacements is the probability density a maximum for a state of a harmonic oscillator with v = 1? (Express your answers in terms of the coordinate y.)arrow_forwardIf we have two operators A and B possess the same common Eigen function, then prove that the two operators commute with each otherarrow_forward
- Consider both a finite potential well and an infinite potential well. When inside the boxes, may particles be stationary? Explain why.arrow_forwardDraw an energy level diagram for a nonrelativistic particle confined inside a three-dimensional cube-shaped box, showing all states with energies below 15· (h2/8mL2). Be sure to show each linearly independent state separately, to indicate the degeneracy of each energy level. Does the average number of states per unit energy increase or decrease as E increases?arrow_forwardShow that the function ψ = 8e5x is an eigenfunction of the operator d/dx. What is the eigenvalue? Prove that the momentum operator corresponding to px is a Hermitian operator. Show solutions please. thanks!arrow_forward
- The condition of the rigid boundaries demands that the wave function should vanish for x=0 and for x=L because?arrow_forwardFind the Probability (in %) that a particle trapped in a box, L units wide can be foundbetween 0.25L and 0.5L for the ground state.Normalize the wave function given by ψ (x) = A exp(−ax2) over the domain −∞ ≤x ≤ +∞ where A and a are constants.arrow_forwardIf you double the width of a one-dimensional infinite potential well, (a) is the energy of the ground state of the trapped electron multiplied by 4, 2, , , or some other number? (b) Are the energies of the higher energy states multiplied by this factor or by some other factor, depending on their quantum number?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningUniversity Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax