Why is the momentum operator (Px) sometimes given as -i(hbar)(d/dx) while i've seen it also (hbar/i)(d/dx)?
Why is the momentum operator (Px) sometimes given as -i(hbar)(d/dx) while i've seen it also (hbar/i)(d/dx)?
Show that momentum space is equivalent to position space knowing that the operator X̂=i(hbar)(∂/∂p). ( ∫(-∞ --> ∞) Ψ•(x) x Ψ(x)dx = ( ∫(-∞ --> ∞) Φ•(p) (i(hbar)(∂/∂p)) Φ(p)dp Please show detailed steps. Thank you.
3. (18 points) The angular momentum operator in the y direction is given by: ly- while the position operator in the x direction is given by: & x. a. (10 points) Determine the commutator for these operators when applied to the dummy function f(x). b. (8 points) What does the value of the commutator tell us about the relationship between the quantum mechanical observables associated with these two operators? Explain
3. (18 points) The angular momentum operator in the y...
1. Show y = sin ax is not an eigenfunction of the operator d/dx, but is an eigenfunction of the operator da/dx. 2. Show that the function 0 = Aeimo , where i, m, and A are constants, is an eigenfunction of the angular momentum operator is the z-direction: M =; 2i ap' and what are the eigenvalues? 3. Show the the function y = Jź sin MA where n and L are constants, is an eigenfunction of the Hamiltonian...
qm 09.2
2. (i) In one dimension, the momentum operator is given by d Ô = -ih- dx Determine the x dependence of the (un-normalised) momentum eigenfunction for a particle of momentum p, free to move along the x axis. [4 marks] (ii) A particle that is free to move along the x axis is described by a wavefunction v(x) = 1/ va, 0, |x<a/2 1x1 >a/2. (a) Show that the probability of measuring a momentum between p and p...
qm 09.3
3. An operator  is Hermitian if it satisfies the condition $ $(y) dx = (Ap) u dx, for any wavefunctions $(x) and y(x). (i) The time dependent Schrödinger equation is ih au = fu, at where the Hamiltonian operator is Hermitian. Show that the equation of mo- tion for the expectation value of any Hermitian operator  is given by d(A) IH, Â]), dt ħi i = where the operator  does not depend explicitly on time....
a) Discuss why the de Broglie wavelength λ corresponding to a momentum p (p wavenumber given by k # 2n/A) leads to a representation of p by the operator p as (h/) (d/dx) hk, where k is the b) Using theoperao orm of p given in part a, show that,pih c) The total energy of a simple harmonic oscillator of mass M and spring constant K can be written as H- p2/M + ke . If the mass is displaced...
Show that the angular momentum operator, Îz = (ħ/i) d/dφ, is hermitian. Hint: consider the wavefunction ψ(φ), where φ varies from 0 to 2π
3. Consider a rigid rotor whose Hamiltonian is given by H L2(21) where L is the angular momentum operator and I is the moment of inertia of the rotator. Its rotation is described by a wave function: (0, N{Yo0(0,6)(1 3i) Y1-1(0,6) 2 Y21(0.0) Y20(0.) Find the normalization constant, N. (i) Find the probability to occupy state Yo0- (ii Find the expectation value of L2 of this state (iii Find the expectation value of L2 of this state (iv) Find (L2L2/21...
Given a utility function U(x,y) = xy. The price of x is Px, while the price of y is Py. The income is I. Suppose at period 0, Px = Py = $1 and income = $8. At period 1, price of x (Px) is changed to $4. Compute the price effect, substitution effect, and income effect for good x from the price change.
Please help me figure out how to take the derivative of "Y" in
respect to "PY" of this equation. I've been trying to
figure it out for a while, but I can't figure it out.
Also, I do know that the answer is provided here. While I know
the answer I'm not quite following how they did what they did. I
think I understand how they got the first part of the answer.
However, I'm totally lost on how they...