An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter A.2, Problem 8P
(a)
To determine
The relation between constant k to the particles momentum.
(b)
To determine
To Show:If a particle has such wave function then it is equally likely to find the particle at any position.
(c)
To determine
To Explain: The constant A must be infinitesimal if this formula is to be valid for all
(d)
To determine
To Show: The given wave function satisfies the differential equation
(e)
To determine
To show: the function
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The normalization condition for a wavefunction Ψ(x, t) is given by
�
∞
−∞
Ψ∗(x, t)Ψ(x, t)dx = 1.
This necessarily means that the LHS has to be independent of time. Show
that this is indeed the case
A definite-momentum wavefunction can be expressed by the formula W(x) = A (cos kx +i sin kx), where A and k are constants.
How is the constant k related to the particle's momentum? (Justify your answer.)
An observable, q, is represented by an operator, . Assuming a system is in a state Ψ(x,t). a) Write an expression for the expectation value of the observable,<q>. b) Write an expression for the uncertainty in measuring the observable, ∆q. c) Write expressions for the operators relating to position and momentum ( and ) and for the squares of these operators. d) If Ψ(x,t) is an eigenstate of , write an equation relating the eigenvalue and itsoperator.
Chapter A Solutions
An Introduction to Thermal Physics
Knowledge Booster
Similar questions
- Can we simultaneously measure position and energy of a quantum oscillator? Why? Why not?arrow_forwardShow that if Ψ it is a function of the type: Ψ(x±v0t) then Ψ satisfy the wave equation shown in the figure. where v0 is the phase velocity of the wave. Hint: write Ψ(x±v0t) = f(u) where u = x±v0tarrow_forwardConsider a particle described by the following wavefunction for all values of ™: 0 (t, x) - N exp{-10²²) exp{-1 wt} ar²} = where a = mw/h, and where m, N and w are constants. Now do the following: a) Determine the energy of this particle, E.arrow_forward
- Calculate the probability that an electron will be found (a) between x = 0.1 and 0.2 nm, (b) between 4.9 and 5.2 nm in a box of length L = 10 nm when its wavefunction is Ψ = (2/L)1/2 sin(2πx/L). Treat the wavefunction as a constant in the small region of interest and interpret δV as δx.arrow_forwardShow that if Ψ it is a function of the type: Ψ(x±v0t) then Ψ satisfy the wave equation shown in the figure. where v0 is the phase velocity of the wave. Hint: write Ψ(x±v0t) = f(u) where u = x±v0t then use chain rule to find the second derivatives that appear in the wave equation.arrow_forwardThe wavefunction for the motion of a particle on a ring can also be written ψ = N cos(mlϕ), where ml is integer. Evaluate the normalization constant, N.arrow_forward
- Problem 1. Using the WKB approximation, calculate the energy eigenvalues En of a quantum- mechanical particle with mass m and potential energy V (x) = V₁ (x/x)*, where V > 0, Express En as a function of n; determine the dimensionless numeric coefficient that emerges in this expression.arrow_forwardProblem 1: (a) A non-relativistic, free particle of mass m is bouncing back and forth between two perfectly reflecting walls separated by a distance L. Imagine that the two oppositely directed matter waves associated with this particle interfere to create a standing wave with a node at each of the walls. Find the kinetic energies of the ground state (first harmonic, n = 1) and first excited state (second harmonic, n = 2). Find the formula for the kinetic energy of the n-th harmonic. (b) If an electron and a proton have the same non-relativistic kinetic energy, which particle has the larger de Broglie wavelength? (c) Find the de Broglie wavelength of an electron that is accelerated from rest through a small potential difference V. (d) If a free electron has a de Broglie wavelength equal to the diameter of Bohr's model of the hydrogen atom (twice the Bohr radius), how does its kinetic energy compare to the ground-state energy of an electron bound to a Bohr model hydrogen atom?arrow_forwardA particle is described by the following wavefunction Ψ1(x) =−b(x2−a2)2: 0≤ x ≤a Ψ2(x) = (x2−d2)−c: a≤ x ≤w Ψ3(x) = 0: x > w Using the continuity condition of an acceptable wavefunction at x = a, find c and d in terms of a and b. Find w in terms of a and b.arrow_forward
- A particle confined in a one-dimensional box of length L(0<=x<=L) is in a state described by the wavefunction Ψ(x)= Ψ1+ Ψ2(x). Where A and B are constants given by real numbers and A>=0.(With X=6 and Y=3)l)Determine what relationship A and B must satisfy for the wavefunction to be normalized.ll)Suppose that A=B .What is the probability of the particle being found in the interval 0<=x<=L/2?lll)What values of A and B that minimize the probability of finding the particle in the range of positions 0<=x<=L/2?arrow_forwardThe wavefunction of an electron is given by 1≤x≤ 16 y(x) = c = 0 x 16 where c is a positive real number. (a) Calculate the probability of finding the electron in the range 2 ≤ x ≤ 11. (b) Where is the electron most likely to be found in the range 1 ≤ x ≤ 16? Explain your answer briefly, with one or two sentences only.arrow_forwardWHY DOES THE WAVE- FUNCTION GO TO ZERO AS X GOES TO * INFINITY ?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 Learning
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
University 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
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax