Recent content by blue_leaf77

Actually the function ##\exp(1000\frac{\sin x}{x})## approaches unity as x goes to ##\pm \infty## which means its integral over all space is divergent. On the other hand the integral over all space of the approximated function as suggested above is convergent.

In this context, (anti)symmetry with respect to particle exchange.

They are orthogonal if ##X_-^\dagger X_+ = 0## (or alternatively ##X_+^\dagger X_- = 0##).

At least in the field of photoionization, the energy distribution can be obtained from angular distribution by integrating the latter over all angles.

Taking analogy with the position operator counterpart, ##1/r##, the first thing about this operator is that its spectrum lies in the positive half of the axis. Your reciprocal ##p## operator does not seem to have this property, it might help defining it with an absolute sign ##|p|##. Second, the...

In addition to the various hints everyone here has tried to lead the OP with, any three random points which are mutually not coinciding and not all situated along a single line uniquely define a plane.

I think we need to be careful here especially in the use of the term "system". For instance if we take as an example of the "whole system" to be the electrons in an atom whose total spin is an integer, the wavefunction of the whole system i.e. the system of all electrons inside this atom will...

I am having trouble trying to understand the quantity ##S(\rho)##, is it a scalar or matrix and how does it differ from ##S##? Moreover since the thing in the middle of is just a number, shouldn't it be possible to write it as \begin{align*}...

If you have access to quantum chemistry package I would suggest that you try restricted Hartree-Fock calculation. Usually it predicts the correct configuration (i.e. it yields the lowest single configuration energy) as that used as general rule of thumb.

If you calculate the expectation value of number operator, does it not give you at least the idea about how many particles we have?

As far as I know there are two ways to have your computer running on linux and something else (e.g. MacOS or Windows): dual boot or virtual machine. The first one has been pointed out by Scott above and it requires you to partition your harddisk. In this method both OS's exist on the same level...

My memory about the solution of Laplace's equation is a bit hazy but after checking wikipedia about spherical harmonics, the general solution of this equation takes the form of $$ \psi(r,\theta,\phi) = \sum_{l=0} \sum_{m=-l}^l c_{lm} r^l Y_{lm}(\theta,\phi) $$ which is clearly not normalizable...

f(x+h) = -x-h

Any vector is a rank-1 tensor. If it's a vector operator like spin operator then it can also be called a rank-1 tensor operator.

For the ones used in actual applications, not quite so. It's true that a hollow cable having reflective inner surface can also transmit light from one end to the other but such scheme proves to suffer from high amount of loss per unit distance (I either read it somewhere or heard it from someone...