Determine the result of measuring
and
for an electron with a wave-function corresponding to the "spin
up" state.
Determine the result of measuring and for an electron with a wave-function corresponding to the "spin...
Consider a wave function for a hydrogen-like atom: 81 V πα3 a) Find the corresponding values of the quantum num bers n, 1, and m. (b) By measuring the angular momentum, what is the probability of finding 1-0? (c) Construct ψ(r, θ, φ) and another wave function with the same values of n and (azimuthal) quantum number, m+1 (d) Calculate the most probable value of r for an electron in the state corresponding to ψ(r, θ, φ) 1, but with...
4. Spin (10 marks) Suppose an electron is in a state such that its spin can be described by a linear superposition of the eigenspinors of S +A 32 2/22 (a) Normalise the state. (b) What are the possible outcomes of a measurement of the z-component of the spin? What is the probability of each possible result? (c) What are the expectation value and uncertainty of the z-component of the spin? (d) What are the possible results of measuring the...
- A() An electron is in the spin state x= A Determine the normalisation constant 1 i A, and then find the expectation value of the z-component of the spin operator h [6]
6. (16 pts) Fill in the blanks a) The idea of electron spin was introduced after experiments had shown that electron energy levels in an atom are affected by b) The evidence for 2 spin states, labeled spin up & spin down, was provided by the S experiment in which silver atoms (IKr]4d105s) were and the observed result was c) The selection rule for optical transitions is e- d) The allowed values of ( are e) The allowed values of...
ILUULLUHUJJ. U TILI JL CUILIUI " J.. 3) Two-electron system: Consider a two-electron system. The spin-orbitals are denoted by Wiolj = 0;\; X.;) where i is the orbital quantum number, o is the spin quantum number, r; and s; are the space and spin coordinates of the ith electron. The composite wave function is in a state given by: 114.2) 42.2 4.2) 2.2 (a) Find A. (b) Show that y 1,2 can be separated into space and spin components, i.e....
Spin Wave Function
For a system consisting of two electrons,
Show that either tye symmetric function or the antisymmetric
function is an eigenfunction of the total spin operator ,S^2
What is the eigenvalue for the wave function you chose?
For a system consisting of two electrons, show that either the symmetric function ψ.-1(d)β(2) + a(2g(1)] or the antisymmetric function: is an eigenfunction of the total spin operator, 32 What is the eigenvalue for the wave function you chose?
For a...
An electron is in the spin state x= A () (a) Determine the normalization constant A. (b) Find the expectation values of Sx , Ŝ, and Ŝ. (c) Find the “uncertainties” Ost, Os, and os, (d) Confirm that your results are consistent with all three uncertainty principles.
[5] A large number of spin-1/2 particles are run through a Stern-Gerlach machine. When they emerge. all particles have the same spin wave function s)- (where the vector representation is in the basis set of eigenvectors of Sz. The spin of the particles is measured in the z-direction. On average, 2/3 of the particles have spin in the +z direction and 1/3 in the z direction. (a) Determine one possible normalized spin wave functio tere a single unique solution to...
The image below shows the wave function of an electron in a rigid box. The electron energy is 15.3eV. What is the energy of the electron's ground state? Submit Answer Tries 0/10 (x)
2 The wave function describing a state of an electron confined to move along the X-axis is given at time zero by Y(x,0) = Ae/ Determine, in terms of A and dx, the approximate probability of finding the electron in an infinitesimal region dx centered at a) x 0 b) x a, and c) x 2a dy In which region is the electron most likely to be found? (25 pts)
2 The wave function describing a state of an electron...