Question 1: In a region of space, a particle with mass 'm' is moving in a...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Question 1: In a region of space, a particle with mass 'm' is moving in a non-zero potential field (V) #0). Axe 12 The time independent wave function of the particle can be represented as Px) (Where A and L are constants). Using the above wave function, write the complete Schrodinger's wave equation for the above particle. If the total energy (E) of the particle becomes zero, determine the potential energy (V) of the particle. (а) (b) Question 2: Show, which of the following is (are) eigenfunction(s) of the linear momentum operator, Pand if so what is (are) eigen value(s). P(x) = A sin(kx) – A cos(kx) P(x) = A cos(kx) + iA sin(kx) (a) (b) Note: A andk are constants. Question 3: Complete the following statement with an appropriate equation. (a) (b) The wave function is normalized if, The wave function fx) and g(x) are orthogonal if, The wave function P) Operator, Ä, is a linear operator, if, Operators, A and B, commute with each other, if, Operator, 0, is an Hermitian operator, if (c) is an Eigen function of the operator, Ä, if, (d) (e) (f) Question 5: For a particle in a one-dimensional box, the obtained final eigenfunction was of the form, y = A sin(kx). Explain why we could not use the following wave functions: (i) y = Ae' (ii) y = Acos(kx) Question 1: In a region of space, a particle with mass 'm' is moving in a non-zero potential field (V) #0). Axe 12 The time independent wave function of the particle can be represented as Px) (Where A and L are constants). Using the above wave function, write the complete Schrodinger's wave equation for the above particle. If the total energy (E) of the particle becomes zero, determine the potential energy (V) of the particle. (а) (b) Question 2: Show, which of the following is (are) eigenfunction(s) of the linear momentum operator, Pand if so what is (are) eigen value(s). P(x) = A sin(kx) – A cos(kx) P(x) = A cos(kx) + iA sin(kx) (a) (b) Note: A andk are constants. Question 3: Complete the following statement with an appropriate equation. (a) (b) The wave function is normalized if, The wave function fx) and g(x) are orthogonal if, The wave function P) Operator, Ä, is a linear operator, if, Operators, A and B, commute with each other, if, Operator, 0, is an Hermitian operator, if (c) is an Eigen function of the operator, Ä, if, (d) (e) (f) Question 5: For a particle in a one-dimensional box, the obtained final eigenfunction was of the form, y = A sin(kx). Explain why we could not use the following wave functions: (i) y = Ae' (ii) y = Acos(kx)
Expert Answer:
Related Book For
University Physics with Modern Physics
ISBN: 978-0321501219
12th Edition
Authors: Hugh D. Young, Roger A. Freedman, Lewis Ford
Posted Date:
Students also viewed these chemistry questions
-
A uniform electric field exists in a region of space in which there are no charges. What can you conclude about the net electric flux through a Gaussian surface placed in this region of space?
-
Please assist with the following problem: Xonic Graphics currently offers 2/10 net 60 credit terms. Please explain each of the changes below as to whether the change will increase or decrease sales:...
-
If the electric field in a region of space is zero, can you conclude that no electric charges are in that region? Explain.
-
1. Johnathan's utility for money is given by the exponential function: U(X)-4-4*100). a. Based on his utility function, what is his risk-odds for the S+/-1 deal, r($1)? b. Is Johnathan a deltaperson?...
-
y = 6(3)x Graph the equation by hand.
-
(a) If f is continuous on [a, b], show that (b) Use the result of part (a) to show that
-
Find the Fourier series of \(f(x)=x\) on the given interval. Plot the Nth partial sums and describe what you see. a. \(0
-
Tiger Furnishings produces two models of cabinets for home theater components, the Basic and the Dominator. Data on operations and costs for March follow: Required Compute the predetermined overhead...
-
Help with the Lease Amortization Schedule.l Skysang Leasing Compary signs a lease agreement on January 1,2020 , to lease electronic equipment to Sheridan Compary. This is a sales-type lease. The term...
-
Assume the following data for Animal Transport Company REFERENCE REVENUE BUDGET Requirement Prepare a cash budget for April for Animal Transport. Begin the cash budget by calculating the cash...
-
discuss differences between services like AWS LightSail and EC2. Provide what you think are the benefits to each, and which you prefer so far ( should be prefer for beginner ) . Describe also if...
-
Quadrant Ltd has the following results for its three most recent accounting periods: Notes: 1. There were no trading losses brought forward on 1 July 2021. 2. Capital losses brought forward on 1 July...
-
VFD Limited (which is not a group company) has prepared a set of accounts for the ten months to 31 March 2024. These accounts show a pre-tax profit of 1,429,530. Relevant information is: (i)...
-
Antietam Ltd makes up accounts to 30 September annually. Results for the 12 months to 30 September 2023 are as follows: The company has capital losses brought forward from previous accounting periods...
-
The following information is available for Online Ltd for the year to 31 March 2024: Operating profit Online Ltd's operating profit for the year to 31 March 2024 is 896,700. Depreciation of 21,660...
-
Neil has been in business for many years preparing accounts to 5 April each year. His profits in a typical year (adjusted for tax purposes) are approximately 50,000 and his drawings are 3,000 per...
-
Post these transactions from each General Journal into theGeneral Ledger accounts.When posting transactions to the general ledger, use thetransaction letters a, b, c, d, or e as the description for 2...
-
Use the formula to determine the value of the indicated variable for the values given. Use a calculator when one is needed. When necessary, use the key on your calculator and round answers to the...
-
From Pillar to Post Starting from a pillar, you run 200 m east (the + x-direction) at an average speed of 5.0 m/s, and then run 280 m west at an average speed of 4.0 m/s to a post. Calculate (a) Your...
-
Two runners start simultaneously from the same point on a circular 200-m track and run in opposite directions. One runs at a constant speed of 6.20 m/s, and the other runs at a constant speed of 5.50...
-
It was shown in Example 21.11 (Section 21.5) that the electric field due to an infinite line of charge is perpendicular to the line and has magnitude E = /2є0r. Consider an imaginary cylinder...
-
\(P(-2.15
-
\(P(z>-0.74)\). In Exercises 2126, find the indicated probability using the standard normal distribution. If convenient, use technology to find the probability.
-
Yearly amounts of greenhouse gases from U.S. energy sources since 1990 are normally distributed, with a mean of 5774 million metric tons carbon dioxide equivalent (MMT \(\mathrm{CO}_{2}\) eq.) and a...
Study smarter with the SolutionInn App