Shankar Definition and 45 Threads

On page 160 in Shankar, he discusses how we get quantized energy levels of bound states - specifically for the particle in a box. We have three regions in space; region I from ## \ - \infty, -L/2 ##, region II from ## \ -L/2, L/2 ##, and region III from ## \ L/2, \infty ##. For the...

For the case of general potential V(x), what does it mean when he says that there are always one more constraint than free parameters? At each interval, ψ and ψ' must be continuous, so that is 2 constraints at each interval, and I understand that there are 2 parameters of the wavefunction in...

I know how to work through this problem but I have a question on the initial separation of the wave function. Assuming ##\psi(\rho, \phi) = R(\rho)\Phi(\phi)## then for the azimuthal part of the wavefunction we have ##\Phi(\phi)=B\left(\frac \rho\Delta cos\phi+sin\phi\right)##, but this function...

On the Yale University Prof Shankar Youtube vid 'Lorentz Transformation' Prof Shankar writes up on the board that x = ct and then x prime = c t prime. It is the basis of all that follows. But i don't understand. at x = 0, t = 0 and x prime = 0 and t prime = 0. He's got that written up...

I don't see why it is not ##P(\omega)\propto |\langle \psi | \mathbb{P}_{\omega}|\psi\rangle |^2.## After all, the wavefunction ends up collapsing from ##|\psi\rangle## to ##\mathbb{P}_{\omega}|\psi\rangle.##

In about a month or perhaps less I believe I will have finished my reading of Shankar. Which textbooks would you consider to be a next step from that? There are 3 things I would appreciate. One is slightly more mathematical rigour, perhaps something that makes greater use of methods from...

Equation 9.2.25 defines the inner product of two vectors in terms of their components in the same basis. In equation 9.2.32, the basis of ## |V \rangle## is not given. ## |1 \rangle ## and ## |2 \rangle ## themselves form basis vectors. Then how can one calculate ## \langle 1| V \rangle ## ? Do...

Homework Statement Homework Equations definition of null vector, [/B] The Attempt at a Solution null vector : ## |0 \rangle = (0,0,0) ## inverse of (a,b,c) = ( - a, -b, -c) vector sum of the two vectors of the same form e.g. (c,d,1) + ( e,f,1) = ( c+e, d+f, 2) does not have the same...

I am currently taking a second course on QM (at undergraduate level). The official texts of my course are Griffiths (we are covering the second half of it) and Shankar (for everything that is not in Griffiths). But after reading Shankar for a while, I found myself not really liking the book too...

Hello Everyone, I am an undergraduate physics student who planned to study quantum mechanics. I have been reading the introductory book by Griffiths, however I found that his book seldom uses Dirac Notation and there is little about mathematical formalism on quantum mechanics. Therefore I would...

https://www.amazon.com/dp/0521592100/?tag=pfamazon01-20 Yes, this is the same Shankar who wrote the QM book. It is not a pure QFT introduction like his QM book but seems more like QFT's application too Condensed matter.

<Mentor's note: moved from a technical forum, therefore no template.> I'm long out of college and trying to teach myself QM out of Shankar's. I'm trying to understand the reasoning here because I think that I am missing something... 1.1.3 1) Do functions that vanish at the endpoints x=0 and...

Hope this is a valid question. I can't quite understand this very simple thing. Prof Shankar's introduction to relativity on Youtube starting at about 50 minutes has a quick calculation that comes up with the Lorentz transform. I follow the maths, no problem. But he confuses me a bit when...

I've taken Calc I to III and linear algebra, although the course was overall quite light. I don't know what legendre polynomials are, and haven't learned hamiltonians (and probably won't since its not in morin), When i start the book i will have finished david morins mechanics book,tenenbaums...

Can someone help with what must be a simple math issue that I'm stuck on. Shankar ("Principles of Quantum Mechanics" p. 153) evaluates the propagator for a free particle in Equation 5.1.10. A scan of the chapter is available here...

I am hung up on what must be a very elementary matter, but I’m unable to see where I’m wrong. I reference R. Shankar's "Principles of Quantum Mechanics". For the free particle with https://www.physicsforums.com/file:///C:/Users/DANIEL~1.ABR/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png ...

Asked to determine the eigenvalues and eigenvectors common to both of these matrices of \Omega=\begin{bmatrix}1 &0 &1 \\ 0& 0 &0 \\ 1& 0 & 1\end{bmatrix} and \Lambda=\begin{bmatrix}2 &1 &1 \\ 1& 0 &-1 \\ 1& -1 & 2\end{bmatrix} and then to verify under a unitary transformation that both can...

Folks, What is the idea or physical significance of simultaneous diagonalisation? I cannot think of anything other than playing a role in efficient computation algorithms? Thanks

Hello! On p.145 of Shankar's Principles of Quantum Mechanics, the author derives the general propagator for the Schrodinger equation in the following manner. Shankar's working Expanding the state vector in the energy basis, |\psi(t)\rangle = \sum_{E} |E\rangle \langle E| \psi(t) \rangle...

I know there are a lot of similar questions here but just hear me out. I am going to start self-studying quantum mechanics in a few days. I think I am going to use the MIT quantum mechanics 1 lectures as a starting point. But books will be essential as I spend most of my time in school. I have...

Hi I have just bought the hardback version of "Principles Of Quantum Mechanics" by Shankar online. The website stated that it is the corrected version from 2008 but the book has no mention of corrected version 2008 inside it. Does anyone know if the hardback version states inside the book that...

This is solving a coupled mass problem using the techniques used in QM, it's in the mathematical introduction of Shankar. This equation was obtained by using the solution for ##x(t) = x_i(0)cos(\omega _i t)## and plugging it into ##\left| x(t) \right \rangle = \left| I \right \rangle x_i...

Author: R. Shankar Title: Principles of Quantum Mechanics Amazon Link: https://www.amazon.com/dp/0306447908/?tag=pfamazon01-20 Prerequisities: Contents:

Hello there, Im studying QM with Shankar's book. I'm wrestling myself trough the linear algebra now and I have some questiosn. Let me start with this one: I have absolutely no idea where this is coming from or what does it mean. I don't know how to multiply a ket with an inner...

I have the option of doing either a one-semester QM course with Griffiths or a two-semester course with Shankar. Background is Eisberg and Resnick's "Quantum Physics". I really like quantum mechanics and would rather do two semesters, but will Shankar be too formal for an upper-level undergraduate?

All three seem to be loved, mathematically rigorous, and appropriate as undergraduate-level texts. I have a good knowledge of classical physics, ODEs and PDEs, linear algebra and multivar calculus, but no knowledge of analytical mechanics or QM. Some opinions on these or other recommendations...

Homework Statement Show that if H = -\gamma\mathbf{L\cdot B}, and B is position independent, \frac{\mathrm{d} \left \langle \mathbf{L} \right \rangle}{\mathrm{d} t}=\left \langle \boldsymbol\mu \times\mathbf{B} \right \rangle=\left \langle \boldsymbol\mu \right \rangle\times\mathbf{B} Here H...

Hi, Im studying a book "Principles of Quantum Mechanics" by Shankar. Im in the fifth chapter, Simple Problems in One dimension. In page 169 to 170, the book says about the standard procedure for finding the fate of the incident wave packet. But i don't understand why we are finding...

Shankar 12.4.4 - "the" rotation matrix vs. "a" rotation matrix (tensor operators QM) Homework Statement My question comes up in the context of Shankar 12.4.4. See attached .pdf. Homework Equations See attached .pdf The Attempt at a Solution See attached .pdf I have this...

Hi everyone, I am really stuck here, and I would really appreciate if someone could help me out. The statement of the problem is attached as a image. Some equations referred by the problem are also attached in another image. I will try to explain how I have reasoned using more words than...

First, I appologise if this is in the wrong place, while the book is QM, the question is pure maths. Also I'm not sure if this techically counts as homework as I am self studying. Finally, sorry for the poor formatting, I'm not that good with LaTeX Homework Statement Given the matrix...

Has anybody read/use both these books? Which one is "better"? Thanks.

Hi, I have a pretty strong background in quantum and I've already gone through sakurai using shankar as a reference for courses and such. However, this summer, I want to go through a comprehensive quantum book cover to cover in preparation for going through Zee's QFT book. Which do people...

Hi, On p67 of shankar Principles of QM, he considers the delta functions derivative. He says: \int \delta'(x-x')f(x')dx'= \int \frac{d\delta(x-x')}{dx}f(x')dx'= \frac{d}{dx}\int \delta(x-x') f(x')dx'=\frac{df(x)}{dx} I don't understand how the second equality follows, how can the...

shankar "PQM" is wrong? Shankar Principles of Quantum mechanics Pag 46: Example 1.8.6 The movement equations are in my opinion wrong. Consider the following link for the same equations http://farside.ph.utexas.edu/teaching/315/Waves/node17.html

Homework Statement Two identical bosons are found to be in states |\phi> and |\psi>. Write down the normalized state vector describing the system when <\phi|\psi>\neq0.Homework Equations The normalized state vector for two bosons with <\phi|\psi>=0, using the fact that...

Homework Statement Exercise 5.2.2 (b.) Prove the following theorem: Every attractive potential in one dimension has at least one bound state. Hint: Since V is attractive, if we define V(\infty)=0, it follows that V(x)=-|V(x)| for all x. To show that there exists a bound state with E<0...

Ok, maybe the subject has been discussed in some manner in other posts, but I would like a clear comparison between : * David J Griffiths - Introduction to Quantum Mechanics * Shankar - Principles of Quantum Mechanics * Sakurai - Modern Quantum Mechanics What is your experience with these...

I've started to learn Quantum Mechanics from Shankar's book "Principles of Quantum Mechanics". My qm professor recommended Sakurai to me, but I feel more comfortable using Shankar. What can you tell me about these 2 books? Which one do you prefer?

Homework Statement Particle described by wavefunction psi(r,theta,phi) = A*Exp[-r/a0] (a0 = constant) (1) What is the angular momentum content of the state (2) Assuming psi is an eigenstate in a potential that vanishes as r -> infinity, find E (match leading terms in Schrodinger's...

Homework Statement Could someone get me started with Exercise 2.5.1 in Shankar's Principles of Quantum Mechanics? Does this forum support TeX or LaTeX? Homework Equations The Attempt at a Solution

What are your opinions on Shankar: Principles of Quantum Mechanics and Griffiths: Introduction to Elementary Particle physics? I've decided to use them to study my two QM modules and my Particle Physics Modules, instead of the recommended texts. So how good are they?

Would someone mind opening his or her Shankar page 153 and tell me what (5.1.10) and (5.1.11) exactly mean? Does (5.1.10) stand for a delta function? thank you

Hi, Have to get my Christmas wish lists together and was looking for a good book to buy on QM. I need some background on the mathematics involved. I'm also self-studying, with the help of you all of course :) I found this book to meed my needs, but I'm a bit unsure to spend a lot of...

The question is: 19.5.4 Show that the s-wave phase shift for a square well of depth V0 and range r0 is δ0 = -k r0 + tan-1{(k/k') tan(k'r0)} where k' and k are the wave numbers inside and outside the well. For k small, kr0 is some small number and we ignore it. Let us see what happens...