In this problem we represent the spin eigenfunctions and operators as vectors and matrices a The spin eigenfunctions are often represented as the column vectors Show that Icirc plusmn and Icirc sup2 are orthogonal using this representation b If the spin angular momentum operators are represented by...

a Using the rules of matrix multiplication Therefore and are o ...

In this problem we represent the spin eigenfunctions and operators as vectors and matrices. a. The spin

Question:

In this problem we represent the spin eigenfunctions and operators as vectors and matrices.

a. The spin eigenfunctions are often represented as the column vectors

Show that Î± and Î² are orthogonal using this representation.

b. If the spin angular momentum operators are represented by the matrices

show that the commutation rule [sÌ‚_x ,sÌ‚_y] = ihsÌ‚_z holds.

c. Show that

d. Show that Î± and Î² are eigenfunctions of sÌ‚_z and sÌ‚₂. What are the eigenvalues?

e. Show that Î± and Î² are not eigenfunctions of sÌ‚x and sÌ‚y.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Physical Chemistry

ISBN: 978-0321812001

3rd edition

Authors: Thomas Engel, Philip Reid

See More Books

Question Posted: May 17, 2018 04:21 AM

See More Questions

Using the matrix representation of the operators and spin eigenfunctions of Problem P28.7, show that the relationships listed in Equation (28.20) are obeyed. In Problem 28.7 Given that And Show that...
In this problem, we make all the same assumptions as in Problem 4.75, but we do not discount the flywheel inertia, so our model consists of three inertias, as shown in Figure. Obtain the natural...
Larmor frequencies are usually tens or hundreds of MHz, but to make the numbers easier to handle in this problem we will assume that the Larmor frequencies are very much smaller. Consider a system of...
Accounting for Contingencies and Provisions In accounting, contingencies and provisions play a crucial role in preparing financial statements and ensuring accurate representation of a company's...
A cellular telephone tower that is 120feet tall is placed on top of a mountain that is 1200feet above sea level. What is the angle of depression from the top of the tower to a cell phone user who is...
What is the public for a general view of a system; who would be interested in reading it?
Let $D$ denote the event that you have the illness, and let $S$ denote the event that the test signals positive. The probability requested can be denoted as $P(D \mid S)$. The probability that...
Consider the following data regarding Orange Countys photocopying requirements. The county administrator is trying to decide whether to replace the old equipment. Because of rapid changes in...
Consider three incomes: $35 000, $65 000, and $130 000. Determine the maximum RRSP contribution and the tax benefit at each income level. What would be an equivalent TFSA contribution? Next project...
For the BJT cascade amplifier of Fig. 5.176, calculate the dc bias voltages and collector current for each stage. +15 V 5.1 kQ 24 k 5.1 k 24 k2 0.5 HF If 0.5 pF - 150 6.2 k2 6.2 kQ 50 uF
Calculate the angles that a spin angular momentum vector for an individual electron can make with the z axis.
In this problem you will prove that the ground-state energy for a system obtained using the variational method is greater than the true energy. a. The approximate wave function Î¦ can be...
List some of the reasons why economists should not consider GDP an effective measure of the standard of living in a country.
Describe the difference between primary research and secondary research.
What is the relationship among economics, finance, and accounting?
Inherent risk is: a. the risk the auditor will issue an inappropriate opinion. b. the risk the financial statements are materially misstated without any consideration of controls. c. the only risk...
Is it possible that the market for individual stocks could be highly efficient, but the market for whole companies could be less efficient? Explain.
Why is a pollution regulation regime that is based on emission standards often labelled as a command-and-control approach to pollution control? Be specific.
Is every odd function one-to-one? Explain.
A consultant is beginning work on three projects. The expected profits from these projects are $50,000, $72,000, and $40,000. The associated standard deviations are $10,000, $12,000, and $9,000....
Calculate the probability that a particle will be found between 0.49L and 0.51L in a box of length L when it has (a) N = 1, (b) N = 2. Take the wavefunction to be a constant in this range.
Calculate the expectation values of p and p 2 for a particle in the state n = 1 in a square-well potential.
The mass to use in the expression for the vibrational frequency of a diatomic molecule is the effective mass = m A m B /(m A + m B ), where m A and m B are the masses of the individual atoms. The...
Given the function. f(x) = ln (2x+3x) Compute f'(x). Enter your answer rounded to the nearest tenth
A motor-cycle manufacturing company desires a profit of $600,000. The fixed costs are $800,000. The unit selling price of the motor-cycle is $750 and the variable cost per unit is $680. How many...
3. ZR Corporation's stock has a beta coefficient equal to 0.8 and a required rate of return equal to 11 percent. If the expected rate of return on the market is 12.5 percent, what is the risk-free...

In this problem we represent the spin eigenfunctions and operators as vectors and matrices. a. The spin

Question:

1 and B = %3D ħ(0 1 ħ(1 0 20 -1 -i 2|1 2 i

Step by Step Answer:

a Using the rules of matrix multiplication Therefore and are o...View the full answer

Physical Chemistry

Students also viewed these Sciences questions