Momentum representation, momentum space wave function

We study the relationship between the position space wave function and the momentum space wave function in quantum mechanics. We show that they are related by the Fourier transform, more specifically we show that a momentum wave function given by the Fourier transform of the space wave function satisfies the requirements to be a momentum wave function, that is, normalization (the integral of its magnitude square equals one) and gives the correct formula for the expected value of the momentum.

In the momentum representation, we look for g(p) that satisfies (15.60) and (15.61). As it is claimed there in the attachment, such g can be taken to be the Fourier transform of psi (with the hbar normalization in the definition of Fourier ...

Solution Summary

The solution discusses the momentum representation and the relationship between space wave function and momentum wave function.

At t=0, the wavefunction of a free particle is:
psi(x,0) = {(sqrt b/2*pi)sin(bx) for |x|<((2*pi)/b)
{0 for |x|> or = ((2*pi)/b))
a) What is the probability of finding the particle in the interval 0 less than or equal to x less than or equal to pi/2b?
b) What is the momentum am

Measuring Angular momentum
A particle is in the state with wavefunction shi = 1/sqrt(2)[Y11 + Y1-1]
(a) What value is obtained if L^2 is measured?
(b) Does the particle have a definite value of Lz?
(c) What are the probabilities of getting results h bar and - h bar and 0 for Lz?
Are any other Lz results possible

A 3kg particle has a velocity of (3i-4j) m/s. Find the magnitude of its momentum?
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Answers:
a) 9kg m/s
b) -12 kg m/s
c) 15 kg m/s
d) 3 kg m/s
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A sinusoidal wave is described by y=(0.30m)sin(0.20x-40t). Determine the wave speed.

"A 122 kg astronaut (including space suit) acquires a speed of 2.50 m/s by pushing off with his legs from a 1900 kg space capsule. What is the change in speed of the capsule?"

An object of mass 2 kg travelling in a straight line with a velocity of 20m/sec collides with, and strikes to, a stationary object of mass 3 kg. They both move off together in the same straight line with a velocity of v m/sec. If no external forces are acting calculate
a. the total momentum just before the impact
b. the tot

Question: A 50 kg cart is moving across a friction-less floor at 2 m/s. A 70 kg boy, riding the cart, jumps off so that he hits the floor with zero velocity.
1. What impulse did the boy give to the cart?
2. What was the velocity of the cart after the boy jumped?

Hi, I've attached the problem as a Picture. I've learned a lot from the help I have received here on Brainmass, and I'm going to try doing this one on myself and hopefully I'll do it right. Thank you for your help!
Consider a simple harmonic oscillator with an angular frequency w. Suppose at t=0 it is in a state given by: (se

In an inelastic collision, is the final total momentum more than the initial momentum, less than the initial momentum or is it the same as the initial momentum?

(a) Estimate the uncertainty in the momentum of an electron whose location is uncertain by a distance of 2 Angstrom. What is the uncertainty in the momentum of a proton under the same conditions?
(b) What can one conclude about the relative velocities and energies of the electron and proton in the last problem? Are wave phenom