a Prove that (1 2) (1 ix) acting on a two component spinor can be regarded as the matrix representation of the rotation operator about the x axis by angle 2 (The minus sign signifies that the rotation is clockwise ) b Construct the matrix representation of Sz when the eigenkets of Sy are used as ba...

a The rotation matrix cE 3244 acting on a twocomponent spinor can be For clockwise ro ...

a. Prove that (1/2) (1 + ix) acting on a two-component spinor can be regarded as the

Question:

a. Prove that (1/√2) (1 + iσx) acting on a two-component spinor can be regarded as the matrix representation of the rotation operator about the x-axis by angle – π/2. (The minus sign signifies that the rotation is clockwise.)

b. Construct the matrix representation of Sz when the eigenkets of Sy are used as base vectors.

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

Step by Step Answer:

Related Book For book-img-for-question

Modern Quantum Mechanics

ISBN: 978-0201539295

Revised Edition

Authors: J.J Sakurai

See More Books

Question Posted: Apr 16, 2011 06:41 AM

See More Questions

Elastic lepton scattering (8.1) can be regarded as a special case of inelastic scattering (8.26) in which the final hadronic state X is a single proton. Find the corresponding value of the scaling...
HDD and CDD can be regarded as payoffs from options on temperature. Explain this statement.
Explain why a swap option can be regarded as a type of bond option.
Phoenix Corp. faltered in the recent recession but is recovering. Free cash flow has grown rapidly. Forecasts made in 2016 are as follows. Phoenix's recovery will be complete by 2021, and there will...
The capacitive reactance in an RLC circuit is determined to be 31 when the inductive reactance is 16 . (a) Is the generator frequency v higher or lower than the natural frequency v0? (b) Is the...
What is thermal radiation? How does it differ from the other forms of electromagnetic radiation?
Correlation and $t$-Statistics. Use the following steps to establish a relationship between the correlation coefficient and the $t$-statistic for the slope. a. Use algebra to check that...
McTaggart-Hicks transactions as operating (O), investing (I), financing (F), non-cash investing and financing (NIF), or a transaction that is not reported on the statement of cash flows (N). Indicate...
5. Solve the equations AX=Y, where: 13 -8 -3 [20 X1 10-1,Y=-5, X = X2 A=-8 -3-1 -1 11 0 X3 Attach the results
On November 3, 20X2, PRD Corporation acquired 2 JRS Company bonds ($1,000 face value) at a cost of 105. PRD classifies them as available-for-sale securities. On this same date, PRD decides to hedge...
Consider a three-dimensional ket space. If a certain set of ortho-normal kets?say, | 1 >, | 2 >, and | 1 > ? are used as the base kets, the operators A and B are represented by with a and b both...
Some authors define an operator to be real when every member of its matrix elements } basis in this case). Is this concept representation independent, that is, do the matrix elements remain real even...
What is the inclination of any line perpendicular to the line through the points (2, 1) and (5, 7)?
ToyWorks Ltd. is a company that manufactures and sells one single product. For planning and control purposes they utilize a monthly master budget. Their fiscal year end is December 31. It is October...
How do socio-environmental factors, including social support networks and workplace culture, influence stress perception and coping efficacy?
How do individual differences in personality traits, coping styles, and genetic predispositions influence susceptibility to stress-related disorders and the effectiveness of stress management...
In what ways do physiological interventions, such as biofeedback and progressive muscle relaxation, aid in stress regulation and physiological homeostasis?
During the current year, Carter Company reported $ 5 0 0 , 0 0 0 in sales, and purchased merchandise that cost $ 3 0 0 , 0 0 0 . The company's beginning inventory and ending inventory was $ 6 0 , 0 0...
The Government Accounting Office reported that airlines block new carriers at major airports. a. What effect does such blocking have on fares and the number of flights at those airports? b. How much...
Portal Manufacturing has total fixed costs of $520,000. A unit of product sells for $15 and variable costs per unit are $11. a). Prepare a contribution margin income statement showing predicted net...
Show that I cal/g. C = 1 kcal/kg.C.
We are to add angular momenta j 1 = 1 and j 2 = 1 to form j = 2, 1 , and 0 states. Using either the ladder operator method or the recursion relation, express all (nine) {j,m} eigenkets in terms of |j...
The goal of this problem is to determine degenerate eigenstates of the threedimensional isotropic harmonic oscillator written as eigenstates of L 2 and L z , in terms of the Cartesian eigenstates |n...
(a) Consider a system with j = 1. Explicitly write in 3 x 3 matrix form. (b) Show that for j = 1 only, it is legitimate to replace e -iJy/h by (c) Using (b), prove (j = 1,m'Jy|j = 1,m)
A motorist travels 70 mi while driving in a bad rainstorm. In sunny weather, the motorist drives 30 mph faster and covers 130 mi in the same amount of time. Find the speed of the motorist in the...
Using the following information, prepare the following financial statements in good form: Cost of Goods Sold Statement Multi - Step Income Statement Retained Earnings Statement Classified Balance...
Selected comparative financial statements of Korbin Company follow. KORBIN COMPANY Comparative Income Statements For Years Ended December 31 Sales 2021 $ 559,409 2020 2019 $ 428,553 $ 297,400 Cost of...

a. Prove that (1/2) (1 + ix) acting on a two-component spinor can be regarded as the

Question:

Step by Step Answer:

a The rotation matrix cE 3244 acting on a twocomponent spinor can be For clockwise ro...View the full answer

Modern Quantum Mechanics

Students also viewed these Modern Physics questions