Recent content by hokhani

Is this wave function calculated by Hamiltonian?

Yes. Thanks all. Your comments resolved the ambiguity about internal energy and potential energy.

Does photon have wave function?

The potential by its own is not physicaly meaningful and it is the potential difference which is important. We can choose any point as the origin of potential, i.e, the point at which the potential is zero. By "another point" I meant kind of "another fact".

Usually in elementary physics text book, dealing with energy concept is in such a way that we first choose a reference frame for kinetic energy and an origin for potential energy, then study the system dynamics. But as far as I understood, it seems that for potential energy we must have another...

Thanks, but as I read in some references, internal energy is equal to the sum of the average kinetic and potential energies of all molecules. So, at higher places the potential energy of particles increases and hence, the internal energy must increase. Otherwise I think this definition of the...

Suppose that we just put a cylinder of an ideal gas in a higher place. Does it's internal energy increase?

The notes you sent formalizes the time reversal in a nice approach in accord with Sakurai. The many body book of Bruus is a good reference which covers condense matter topics. However, in spite of several editions it contains a few such problems. Do you know any other alternative text at this...

I think if we accept the complex conjugation only acts on the numbers there is no ambiguity in this term, because at least the explicit form of the operator is clear. In contrary, the form of ##H^*## is representation-dependent and while the representation is not specified, there is no sense of...

Eq. (7.18) in the text, introduces the time reversal dependent Hamiltonian as: ##H\psi(r)=[-\frac{1}{2m}(\nabla_r+ieA)^2+V(r)]\psi(r)##. So, here ##H## is in the positon space as ##H=H_r=\langle r|\hat{H}| r \rangle.##

Right, since in that text the Hamiltonian were represented in position space where ##H_r## is diagonal, I implicitlly assumed diagonal q-representation for ##\hat{H}## as well as properties of ##\Theta##, ##\Theta(c|q\rangle)=c^*|q\rangle##.

Thanks, it was the key point here. If we work in the basis ##|q\rangle## where ##\Theta |q\rangle =|q\rangle##, then we have: ##\Theta H |\rangle=\sum_q H_q^* \langle q|\rangle^* |q\rangle## and ##H\Theta|\rangle=\sum_q H_q \langle q|\rangle^* |q\rangle## so, ##[H,\Theta]=0## corresponds to...

From the Eq. (7.18) in that text, it seems that by ##H## the authors mean the Hamiltonian in the position space. Also, as I remember, it was discussed previously in one of my last threads that ##H## is an operator and writing in the functional form ##H(variable)## doesn't make sense.

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016...

Thanks: right, your method was very nice, but I would like to try this method which still I am stuck in that.