Recent content by keyzan

Is everything ok? Can I continue with the exercise? Although this zero contribution to the first order of perturbation theory seems a bit strange to me

2. Determine the shift of the energy of the ground state to the first order of the theory of perturbations in ##\lambda##. Solution: At the first order of perturbation theory we have that the energies will be: ##E_n (\lambda) = E_n^{(0)} + \langle \phi_n| \beta W|\phi_n \rangle +...

Hello there, I'm training with some exercises in view of the July test, so I will post frequently in the hope that someone can help me, since the teacher is often busy and there are no solutions to the exercises. A particle of mass m in one dimension is subject to the potential: ##V(x) =...

Ye I forgot to insert the variable t. So is ##\psi(x,t)##. I studied Ehrenfest's theorem. I know that to go from the Shroedinger representation to the Heisenberg one (where the states do not evolve but the operators), you need to use the time evolution operator: ##\hat{A}_H(t) = \hat{U}^+(t...

Hi guys, today I would like to continue solving the exercise. The second point reads: 2. Determine the average value of the position at generic time t. My solution: I expand the following formula: ##\langle\psi\rangle = \langle\psi|\hat{X}|\psi\rangle = \frac{1}{2} \text{ }[ \langle 1| +...

This is just spectacular

You're absolutely right, I forgot a 2. Everything is much clearer now. So the probability of finding the particle to the left of the hole is very small compared to that of finding it to the right. I'll try to guess: this term, however, should oscillate when we insert the times, because, while...

Ok so I can say that the probabilities of finding the particle in the entire hole in the states: ##P(1) = \frac{1}{2}## ##P(2) = \frac{1}{2}## So the probability of finding it in the left or right half of the hole is: ##P(1) = \frac{1}{4}## ##P(2) = \frac{1}{4}## (I find the same result by...

Hi guys it's me again. I need help with this exercise which reads: a particle of mass m, placed in an infinite rectangular one-dimensional potential well that confines it in the segment between ##x = -\frac{a}{2} and x=\frac{a}{2}##, is at instant ##t=0## in the state: ##|\psi \rangle =...

The problem here is that the first point tells me to find N using the normalization condition. I found N by integrating the square modulus of the function from minus infinity to plus infinity and the result i found is: ##N = \sqrt{\frac{8}{5a}}## But then the second point tells me: Now I...

I understood what I was doing wrong... When I use the formula: ##P(E_1) = \frac{|c_1|^2}{|c_1|^2+|c_2|^2}## I obviously have to do the complex conjugate of each term. So I get: ##P(E_1) = \frac{\frac {8}{5a}}{\frac {8}{5a} + (\sqrt{\frac {8}{5a}}*\frac{i}{2}+(-\sqrt{\frac {8}{5a}}*...

Mmh.. The sum of the probabilities is different from 1.. So should I enter another normalization constant? (Initially I thought: I just calculated a normalization constant for this purpose!!!. But actually the previously calculated N should not normalize in the case in which we consider the...

Thanks for the feedback. The second point reads: 2. Determine the possible outcomes of an energy measurement and the related probabilities To do this I transformed the sines and cosines: ##\psi(x) = \sqrt{ \frac {8}{5a}} \frac {e^ { \frac {i \pi x}{a}} + e^ { -\frac {i \pi x}{a}}}{2} (1 +...

Hi guys i have this exercise: A particle of mass m, confined in the segment -a/2 < x < a/2 by a one-dimensional infinite potential well, is in a state represented by the wave function: 1. Determine the constant N from the normalization condition. To do this, I have to integral the square...

Is the expectation value of the observable P as you can see from the formula. Ok I said heresy. I obviously can't do this cause we're talking about operators.. I think I just need to solve the integral: $$ \int_{-\frac {a} {2}}^{\frac {a} {2}} \psi^*(x) \space \hat P \space \psi(x) dx \, =...