Recent content by Ibraheem

For an infinite system of coupled oscillators of identical mass and spring constant k. The matrix equation of motion is \ddot{X}=M^{-1}KX The eigenvectors of the solutions are those of the translation operator (since the translation operator and M^{-1}K commute). My question is, for the...

I was not being precise enough in the second comment. ##\langle x|x \rangle= \delta(x-x)=\delta(0)## I should not have said total probability. What I meant was relative probability since it can never be normalized to 1. So it is physically meaningless, I guess. I am asking this just to clarify...

Sorry what I meant was this $$\langle x|x \rangle= \delta(x-x)=\delta(0)$$ is the total probability But $$\langle x|\psi\rangle$$ is a wave function $$\psi(x)$$ so is it correct to say $$\langle x|x' \rangle= \delta(x-x')$$ is a wave function too ??

If I have a general (not a plain wave) state $$|\psi\rangle$$, then in position space : $$\langle \psi|\psi\rangle = \int^{\infty}_{-\infty}\psi^*(x)\psi(x)dx$$ is the total probability (total absolute, assuming the wave function is normalized) So if the above is correct, does that mean...

I actually think I misquoted him. However in either case, this is what made me look into it. I was trying to insert the identity operator in ##XP|\psi>##, where X and P are the position and momentum operators respectively. I first inserted it between X and ##|\psi>## and I got the following...

Yes.

So the second equation is wrong. That's odd since this is what Shankar says , at least according to my understanding, in page 64(Principals of Quantum Mechanics)

Hello, I know that the derivative of Dirac-delta function (##\delta'(x-x') = \frac{d}{dx} (\delta(x-x')))## does the following: ##\int_{-\infty}^{\infty}\psi(x')*\delta'(x-x') dx' = \frac{d\psi(x)}{dx}## it is easy to visualize how the delta function and the function ##\psi(x')## interact along...

Assuming you meant |x'i> = (1/√Δ)|xi>.That means you changed the basis to this new basis corresponding to each discrete step xi. I understood the first part of why <x'i|x'j> equals the delta function and how this new basis vectors are of an infinite length, mainly because of 1/√Δ goes to...

Thank you so much for taking the time to reply and explain this. But I have a one question. when you used Δx'j to define Δx'j = Δ, did you mean Δx'j as the difference in x'j? And could you clarify by what you mean with lattice. Also here: did you mean |x'i> = (1/√Δ)|xi>? because if it was...

Okay, but if I partition the interval into small subintervals of length ##\Delta=\frac{L}{n+1}## and use an approximation to the two functions with discrete functions call it ##f_n(x)## and ##g_n(x)## where these evaluate to points at the right end of each subinterval i.e ##x_i = i\Delta## then...

I am new to quantum mechanics and I have recently been reading Shankar's book. It was all good until I reached the idea of representing functions of continouis variable as kets for example |f(x)>. The book just scraped off the definition of inner product in the discrete space case and refined it...

But how is this energy returned?In other words, where does it exactly go when the magnetic field collapses? I know it was first used to set up a magnetic field, but is it used to push charge in the wire when the power is negative?

So does this mean the inductor returns its energy to the source only when it is inducing a current in the direction of the AC polarity?In other words, the inductor returns its energy to the source when the current induced is in the direction of the decreasing(not yet reversed) current in the...

Hello, In my textbook, it says that if we have a pure inductor connected to an AC source, the average power is zero. It explains that this is because the energy is used to create a magnetic field for the inductor and then it is extracted to the AC source. So how is it possible for the...