with regards. Thanks you.
3. If (:) is a wave function in which the expectation value of the momentum is...
2. Find the expectation value for <p2 > for the ground-state wave function of the infinite 1-d square well. Here p = -i(hbar) d/dx is the (linear) momentum operator
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Assume that electron in area electric field of proton and in the state wave function r + 2p2 1,0.0 1) Find expectation value of energy 2) Find expectation value of angular momentum squared (L2) 3) Find expectation value of angular momentum in component axis -Z L) 4) How much angular momentum in component axis-Z will probability of found particle? And why?
Assume that electron in area electric field of proton...
2.3 The wave function of a harmonic oscillator with the parameters m and w is a superposition of n 0 and n 2 stationary states o(Z,x ), 〈p), 〈d V(x)〉 (5 points) (a) compute the expectation values (r (b) find the expectation value and the variance of the total energy, Which value of the energy you can actually get when doing measurements and with which probability? (5 points)
A. Momentum space We define the momentum space wave function φ(p) as where Ψ(x)is a solution of the Schrödinger equation in configuration (position) space a) Show that the expectation values of and p can be written in terms of Ф(p) as <p(p)p(p)dp b) Demonstrate that φ(p) is normalized, ie if Ψ(x) is normalized. J ΙΨ(2)12dr-1 c) Show that Ф(p) 2dp can be interpreted as the probability to find a particle with momen tum between p and p+ dp
(10 points) Normalize the wave function: Find the expectation values of (x), (r aj. Ģ) and (p2).
Consider a particle confined to one dimension and positive r with the wave function 0, z<0 where N is a real normalization constant and o is a real positive constant with units of (length)-1. For the following, express your answers in terms of a: a) Calculate the momentum space wave function. b) Verify that the momentum space wave function is normalized such that (2.4) c) Use the momentum space wave function to calculate the expectation value (p) via (2.5)
3. Consider the wave function ψ(x)- 슬 읔 ets, where σ s a real valued constant (a) Calculate the expectation value of K). K (b) Estimate the uncertainty Δ.r and Ap using Δ.1-V (.12)-(A)2. 4. Consider the eigenfunctions of the moment uni operator y p r her (a) Show that p,(r) is an eigenfunction of p with an cigenvalue p. (b) Find the coeflicients. w, in the espansion of (r)( upypp ) using the momentum eigenfunctions.
With what amplitude and frequency does the expectation value of the momentum of a proton (m=1.67x10-27 kg) in a ID box of length 0.02 nm oscillate with time? The particle has the initial wave function Voya- Vioys.
Problem 1 Consider the expectation value of the momentum of a particle to follow from the clas- sical relation da Using the expectation value of position of the particle dt Jo derive the expression for the momentum operator in the position representation, i.e -ih
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...