Start with the two linearly independent solutions to the spatial equation from part (c). Create a...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Start with the two linearly independent solutions to the spatial equation from part (c). Create a linear combination and impose the boundary condition at z = 0 to reduce your two linearly independent solutions to one. Then impose the boundary condition at x = L. You should only be able to satisfy this boundary condition for certain discrete values of k. What are these values of k (index them by an integer ne Z)? Write down a full basis of solutions un(r, t) with our two side boundary conditions imposed! Show that the solutions un(x, t) and u_(r,t) are linearly dependent and thus we only need to consider n = 1, 2,.... Hint (highlight to reveal): [The hi Inspired by Kreyszig, Section 12.6. 2 Start with the two linearly independent solutions to the spatial equation from part (c). Create a linear combination and impose the boundary condition at z = 0 to reduce your two linearly independent solutions to one. Then impose the boundary condition at x = L. You should only be able to satisfy this boundary condition for certain discrete values of k. What are these values of k (index them by an integer ne Z)? Write down a full basis of solutions un(r, t) with our two side boundary conditions imposed! Show that the solutions un(x, t) and u_(r,t) are linearly dependent and thus we only need to consider n = 1, 2,.... Hint (highlight to reveal): [The hi Inspired by Kreyszig, Section 12.6. 2
Expert Answer:
Related Book For
Introduction To Quantum Mechanics
ISBN: 9781107189638
3rd Edition
Authors: David J. Griffiths, Darrell F. Schroeter
Posted Date:
Students also viewed these accounting questions
-
The two linearly independent total energy eigenfunctions for rotation in two dimensions are What is the evolution in time of for each of these solutions? 1 , (0) 1 e and o_(0) 2T |-4 1,
-
Two by Two Basis Show that Is a linearly independent set in M22. Add another vector to the set to make it a basis for M22. 1 01 r0 11 r0 0
-
Show that if u and v are linearly independent vectors, then so are u + v and u - v.
-
47GP: Chapter: CH0 CH1 CH2 CH3 CH4 CH5 CH6 CH7 CH8 CH9 CH10 CH11 CH12 CH13 CH14 CH15 CH16 CH17 CH18 CH19 CH20 CH21 CH22 CH23 CH24 CH25 CH26 CH27 CH28 CH29 CH30 Problem: 1CQ 1MCP 1P 2CQ 2MCP 2P 3CQ...
-
Cardinal Paz Corp. carries an account in its general ledger called Investments, which contained debits for investment purchases, and no credits, with the following descriptions. Feb. 1, 2012...
-
A business has three branches at Coimbatore, Trivandrum and Bangalore. The Head Office at Madras purchases goods and sends them to branches, to be sold at a uniform percentage of profit on cost. The...
-
Purple Company has a current ratio of 2.2 on December 31. On that date its current assets are as follows: Purple Company's current liabilities at the beginning of the year were \(\$ 195,000\) and...
-
Top Company holds 90 percent of Bottom Companys common stock. In the current year, Top reports sales of $800,000 and cost of goods sold of $600,000. For this same period, Bottom has sales of $300,000...
-
7 . The ten year Treasury TIPS yield 0 . 8 1 2 % while the ten year Treasury bond has a yield to maturity of 2 . 6 % . Please explain why there are differences between yields of these two bonds both...
-
In a piston assembly, the specifications for the clearance between piston rings and the cylinder wall are very tight. In a lot of assemblies, let X be the number with too little clearance and let Y...
-
Describe three reasons why an audit is not a guaran- tee of the exactness or accuracy of the assertions or representations in financial statements.
-
Indicate the audit objectives that are accomplished by the following audit procedures: a. Confirmation of the cash bank balance with the bank. b. Analysis of inventory turnover. c. Review of a copy...
-
Describe the composition of the audit team and the responsibilities of its members.
-
Illustrate the expansion or reduction performed on each implicant on a Kmap if the operation changes the implicant. (a) Apply the Espresso EXPAND routine to the following function. \[F(A, B, C,...
-
What is virtual coefficient of friction in a V-belt drive?
-
Telehealth/Telemedicine has been a growing trend. How would you the counselor, use this modality in treatment planning with adolescents with substance use disorders? What are some benefits and...
-
10m solution. If Ka(HA) = 10 then pOH of solution will be [Given : log4=0.6] (A) 6.7 (B) Greater than 6.7 & less than 7.0 (C) Greater 7.0 & less than 7.3 (D) Greater than 7.3
-
Sequential measurements. An operator A, representing observable A, has two (normalized) eigenstates 1 and 2 , with eigenvalues 1 and 2 , respectively. Operator B, representing observable B, has...
-
Rotations on spin states are given by an expression identical to Equation 6.32, with the spin angular momentum replacing the orbital angular momentum: In this problem we will consider rotations of a...
-
A particle in the infinite square well has the initial wave function (a) Sketch (x,0), and determine the constant A. (b) Find (x,t). (c) What is the probability that a measurement of the energy...
-
Why do capital campaigns start with a lengthy silent period? What is the board s role in a successful capital campaign?
-
Draft elevator speeches for Greenpeace, Planned Parenthood, March of Dimes, and the American Institute of Certifi ed Public Accountants (AICPA).
-
Discuss the potential fundraising effectiveness of a board with or without a development committee.
Study smarter with the SolutionInn App