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 3, Problem 3.36P
(a)
To determine
The normalization constant.
(b)
To determine
The expectation value of
(c)
To determine
The ground state wavefunction in momentum space.
(d)
To determine
The expectation value of
(e)
To determine
The uncertainty in position and momentum and whether they satisfy uncertainty principle.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
Consider the function
v(1,2) =(
[1s(1) 3s(2) + 3s(1) 1s(2)]
[x(1) B(2) + B(1) a(2)]
Which of the following statements is incorrect concerning p(1,2) ?
a.
W(1,2) is normalized.
Ob.
The function W(1,2) is symmetric with respect to the exchange of the space and the spin coordinates of the two electrons.
OC.
y(1,2) is an eigenfunction of the reference (or zero-order) Hamiltonian (in which the electron-electron repulsion term is ignored) of Li with
eigenvalue = -5 hartree.
d.
The function y(1,2) is an acceptable wave function to describe the properties of one of the excited states of Lit.
Oe.
The function 4(1,2) is an eigenfunction of the operator S,(1,2) = S;(1) + S,(2) with eigenvalue zero.
Is the function Ψ = xe−x^2/2 an eigenfunction of the operator Aˆ = −∂2/∂x2+ x2 ?
A 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.
Chapter 3 Solutions
Introduction To Quantum Mechanics
Ch. 3.1 - Prob. 3.1PCh. 3.1 - Prob. 3.2PCh. 3.2 - Prob. 3.3PCh. 3.2 - Prob. 3.4PCh. 3.2 - Prob. 3.5PCh. 3.2 - Prob. 3.6PCh. 3.3 - Prob. 3.7PCh. 3.3 - Prob. 3.8PCh. 3.3 - Prob. 3.9PCh. 3.3 - Prob. 3.10P
Ch. 3.4 - Prob. 3.11PCh. 3.4 - Prob. 3.12PCh. 3.4 - Prob. 3.13PCh. 3.5 - Prob. 3.14PCh. 3.5 - Prob. 3.15PCh. 3.5 - Prob. 3.16PCh. 3.5 - Prob. 3.17PCh. 3.5 - Prob. 3.18PCh. 3.5 - Prob. 3.19PCh. 3.5 - Prob. 3.20PCh. 3.5 - Prob. 3.21PCh. 3.5 - Prob. 3.22PCh. 3.6 - Prob. 3.23PCh. 3.6 - Prob. 3.24PCh. 3.6 - Prob. 3.25PCh. 3.6 - Prob. 3.26PCh. 3.6 - Prob. 3.27PCh. 3.6 - Prob. 3.28PCh. 3.6 - Prob. 3.29PCh. 3.6 - Prob. 3.30PCh. 3 - Prob. 3.31PCh. 3 - Prob. 3.32PCh. 3 - Prob. 3.33PCh. 3 - Prob. 3.34PCh. 3 - Prob. 3.35PCh. 3 - Prob. 3.36PCh. 3 - Prob. 3.37PCh. 3 - Prob. 3.38PCh. 3 - Prob. 3.39PCh. 3 - Prob. 3.40PCh. 3 - Prob. 3.41PCh. 3 - Prob. 3.42PCh. 3 - Prob. 3.43PCh. 3 - Prob. 3.44PCh. 3 - Prob. 3.45PCh. 3 - Prob. 3.47PCh. 3 - Prob. 3.48P
Knowledge Booster
Similar questions
- Use the method of separation of variables to construct the energy eigenfunctions for the particle trapped in a 2D box. In other words, solve the equation: −ℏ22m(∂2Φn(x,y)∂x2+∂2Φn(x,y)∂y2)=EnΦn(x,y),−ℏ22m(∂2Φn(x,y)∂x2+∂2Φn(x,y)∂y2)=EnΦn(x,y), such that the solution is zero at the boundaries of a box of 'width' LxLx and 'height' LyLy. You will see that the 'allowed' energies EnEn are quantized just like the case of the 1D box. It is most convenient to to place the box in the first quadrant with one vertex at the origin.arrow_forwardBe *(1) the position operator for a particle subjected to a potential of a one-dimensional harmonic oscillator P mox (Ĥ =+ 2m 2 Evaluate [î(t),î(0)] Heisenberg's chart inarrow_forwardSuppose that you have the functional J (a) = [ f {y (a, x), y' (a, æ); x}dx where y (a, x) = 3x – a cos? (x) and f = (y')². What is the minimum value of J (a)? 97Tarrow_forward
- The first four Hermite polynomials of the quantum oscillator areH0 = 1, H1 = 2x, H2 = 4x2 − 2, H3 = 8x3 − 12x. Let p(x) = 12x3 − 8x2 − 12x + 7. Using the basis H = {H0, H1, H2, H3}, find the coordinate vector ofp relative to H. That is, find [p]H. This is a textbook question, not a graded questionarrow_forwardA particle of mass m moves inside a potential energy landscape U(z) = X|2| along the z axis. Part (a) What are the units of the constant X? Part (b) If the particle has kinetic energy me at the origin at z = 0, where are the classical turning points of the motion?arrow_forward(c) At any time t, a particle is represented by the wavefunction w(x,1)= Ae¨Me-lar where 2 and o are real position constants. (i) Normalize y(x,1) (ii) Determine the expectation value of position and momentum.arrow_forward
- Consider a Maxwellian distribution: f(v) = (a) Find (vx) (b) Find (v²) 1 v² v² (PAV) P ( 15 +52 +12²) exp √π)³ Vin (c) Find (mv²/2) (d) Find the flux l' crossing the YZ plane (Suppose the particle density is n)arrow_forwardShow that the spherical harmonics Y2,2(θ,φ)= ((15/32π)^1/2)*sin(2θ)*e^∓2iφ and Y3,3(θ,φ)= ((35/64π)^1/2)*sin(3θ)*e^∓3iφ are normalized.arrow_forwardConsider the problem: [cput = (Koux)x+au, 0arrow_forwardStarting with the equation of motion of a three-dimensional isotropic harmonic ocillator dp. = -kr, dt (i = 1,2,3), deduce the conservation equation dA = 0, dt where 1 P.P, +kr,r,. 2m (Note that we will use the notations r,, r2, r, and a, y, z interchangeably, and similarly for the components of p.)arrow_forwardA definite-momentum wavefunction can be expressed by the formula W(x) = A (cos kx +i sin kx), where A and k are constants. Show that, if a particle has such a wavefunction, you are equally likely to find it at any position x.arrow_forwardProve that the expression e*/(1+ e*)² is an even function of x.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning