Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 8.3, Problem 8.9P
To determine
To evaluate
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Chapter 8 Solutions
Introduction To Quantum Mechanics
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- Verify that vp=2kBTm.`arrow_forwardFor a one dimensional system, x is the position operator and p the momentum operator in the x direction.Show that the commutator [x, p] = iharrow_forwardThe Brachistochrone Problem: Show that if the particle is projected withan initial kinetic energy 1/2 m v02 that the brachistochrone is still a cycloidpassing through the two points with a cusp at a height z above the initialpoint given by v02 = 2gz.arrow_forward
- Prove the following: if the Hamiltonian is independent of time, then ∆E doesn't change in time. Show work and be explicit to prove the statement.arrow_forwardWhat is the numeric answer to problem #24 on page 293? This is a fairly challenging problem.Just remember that Momentum is conserved __________________arrow_forwardVerify that the Hamiltonian equationH(x, p, t) = T + V = p2/2m + (k/2) (x − v0t)2leads to the same motion as described by the following equation:mx¨'= −kx', where x' = x − v0t.arrow_forward
- (a) What is the momentum of a 2000-kg satellite orbiting at 4.00 km/s? (b) Find the ratio of this momentum to the classical momentum. (Hint: Use the approximation that at low velocities.)arrow_forwardParticle of mass m slides without friction on a wedge of angle alpha and mass M that can move without friction on a smooth horizontal surface,as shown in the figure.Treating the constraint of the particle on the wedge by the method of Lagrange multipliers,find the equation of motion for the particle and wedge.Also obtain an expression for the forces of constraint.Calculate the work done in time t by the forces of constraint acting on the particle and on the wedge.what are the constants of motion for thearrow_forwardTwo particles, each of mass m, are connected by a light inflexible string of length l. The string passes through a small smooth hole in the centre of a smooth horizontal table, so that one particle is below the table and the other can move on the surface of the table. Take the origin of the (plane) polar coordinates to be the hole, and describe the height of the lower particle by the coordinate z, measured downwards from the table surface. Here, the total force acting on the mass which is on the table is -T r^ (r hat). Why?arrow_forward
- Set up the integrals to find the ycoordinate of the center of mass for a region of density (x;y)inside the circle x^2 + y^2 = 4 and below y = sqrt (2)arrow_forwardAs an illustration of why it matters which variables you hold fixed when taking partial derivatives, consider the following mathematical example. Let w = xy and x = yz. Write w purely in terms of x and z, and then purely in terms of y and z.arrow_forward
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