Recent content by Samama Fahim

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This is from Modern Cosmology, Scott Dodelson, Chapter 6. For the part "Show that its energy density dilutes as ##a^{−3}##", following is my attempt: In the equation ##\frac{\partial \rho}{\partial t} = -3H(P+\rho)##, put ##P = \frac{1}{2} \dot{\phi}^2-V(\phi)## and ##\rho=\frac{1}{2}...

9.247 reads ##T \backsim e^{-2\gamma}##, ##\gamma = \frac{1}{\hbar}\int_{x_1}^{x_2}\sqrt{2m(V-E)} dx##

Initially '0' is the upper limit and ##a = \frac{Ze^2}{E}## is the lower limit. With change of variable ##x = \frac{Er}{Ze^2}##, for ##r=0##, ##x=0##, and for ##r=\frac{Ze^2}{E}##, ##x=1##, so 1 should be the lower limit. However, he takes 1 as the upper limit, and without a minus sign. Why is...

(This is from W. Greiner Quantum Mechanics, p. 293 from the topic of Ritz Variational Method) 1) Are ##\frac{\delta}{\delta \psi^{*}}## derivatives in equations 11.35a and 11.35b? If this is so, we can differentiate under the integral sign to get ##\int d^3x (\hat{H}\psi)## in equation 11.35a...

Do symmetric wave functions of this sort form a complete set?

Bosons also have spin. Don't they?

I tried googling the problem statement but nothing relevant came up. Not even close.

Problem statement ends here "Given an answer to part (a) and (b) in this case." What follows is my attempt.

What are ##|\xi>## and ##|\eta>##? Are these single particle states? I don't know where to start since I don't understand the problem statement. The only thing I know is how to write symmetric and antisymmetric wave function. What follows the problem statement in the OP is my attempt.

Yes it is a homework problem. Could you give me a hint where I might start?

It's been assigned by the instructor.

Problem: A system contains two identical spinless particles. The one particle states are spanned by an orthonormal system ##|\phi_k>##. Suppose that particle states are ##|\phi_i>## and ##|\phi_j>## (##i \neq j##). (a) Find the probability of finding the particle in the state ##|\xi>## and...

In the boxed equation, how would you get the right hand side from the left hand side? We know that ##H(1,2) = H(2,1)##, but we first have to apply ##H(1,2)## to ##\psi(1,2)##, and then we would apply ##\hat{P}_{12}##; the result would not be ##H(2,1) \psi(2,1)##. ##\hat{P}_{12}## is the exchange...

The plot shows how ##P(\omega)##, i.e., the probability of transition from a fixed state ##a## to a fixed state ##b## changes with ##\omega##, the driving frequency. If that is correct, then it should be possible for a given driving frequency ##\omega < \omega_0## to provoke a transition between...