Question: Operators can also be expressed as matrices and wave functions as column vectors. The operator matrix acts on the wave function (a, b) according to

Operators can also be expressed as matrices and wave functions as column vectors. The operator matrix

acts on the wave function (a, b) according to the rule

In words, the 2 Ã— 2 matrix operator acting on the two-element column wave function generates another two-element column wave function. If the wave function generated by the operation is the original wave function multiplied by a constant, the wave function is an eigenfunction of the operator. What is the effect of the operator

on the column vectors (1, 0), (0,1), (1,1), and (ˆ’1,1)? Are these wave functions eigenfunctions of the operator? See the Math Supplement (Appendix A) for a discussion of matrices.

( a aa + Bb + Sa + eb

Step by Step Solution

★★★★★

3.52 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Only 1 1 1 1 are eigen... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Physical Chemistry Questions!

In practice, it is often difficult to determine the logarithmic decrement of a system with light damping defined in Prob. 19.128 by measuring two successive maximum displacements. Show that the...

Wave functions like the one in Problem 40.34 can represent free particles moving with velocity v = p/m in the x-direction. Consider a beam of such particles incident on a potential-energy step U(x) =...

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...

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Jupiter Notebook We have covered some of the limitations of single layer neural networks in class, but they are still powerful learning systems that provide a good way to begin learning about how to...

Computational Finance - HW 1 Complete the following problems in your home work groups. All calculations must be done in MATLAB. When the question tells you to report or output an answer, your code...

1411116 - Programming I Assignment #3 Due Date: November 30, 2016 Submission Instructions: Submit your assignment on the blackboard link, corresponding to your Section: Please follow the following...

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

Explain how the principles of quantum mechanics are able address the issues. The development of quantum mechanical theory stems from several issues that could not be addressed by the principles of...

Consider a uniformly distributed thin rod of total charge Q = 500nC and length L = 2mm situated on the x-axis between x = 0 and x = L. A) Calculate the magnitude (N/nC) of the electric field at a...

Consider a pump-pipeline system that delivers water from reservoir A to B with EA = 45.5 m and EB = 52.9 m. The pipe has a length of L = 3,050 m, diameter of D = 0.50 m, and a Darcy-Weisbach friction...

hich equation represents a Pressure - Volume change ( constant T and n ) ? Group of answer choices P 1 V 1 = P 2 V 2 P 2 V 1 = P 1 V 2 = none of the answers are correct =

1 Define GDP and explain why the value of production, income, and expenditure are the same for an economy.

Calculate the ratio of the thermal conductivities of gaseous hydrogen at 300 K to gaseous hydrogen at 10 K. Be circumspect, and think about the modes of motion that are thermally active at the two...

At what pressure does the mean free path of argon at 25C become comparable to the size of a 1 dm 3 vessel that contains it? Take = 0.36 nm 2 .

The rate constant of the reaction H 2 O 2 (aq) + I (aq) + H + (aq) H 2 O(l) + HIO(aq) is sensitive to the ionic strength of the aqueous solution in which the reaction occurs. At 25C, k = 12.2 dm 6...

11. Weir Inc. has a bond in its capital structure that has 20 years to maturity left. The bond has a 9.25% coupon paid annually, sells at a price of $1,000 and has a par value of $1,000. If the...

Question 11 1 pts You are at a coffin convention (that welcomes vampires and non-vampires) with mirrored walls. You know that some vampires can be reflected in mirrors but that most can't; you...

Question 19 The prices of a random sample of homes in four areas of a certain city (Areas A, B, C, and D) were recorded Tries remaining: and the following ANOVA table was obtained, and we would like...