Recent content by td21

Could you recommend books which covers extensively numerical simulation of quantum system, such as hubbard model, ising model and discuss quantum monte carlo method? Ideally this is a book of condensed matter physics.

Let K be any Matrix, not necessarily the hamitonian. Is $$e^{-Kt}\left|\psi\right>$$ equal to $$e^{-K\left|\psi\right>t}$$ even if it is not the the eigenvector of K? I think so as i just taylor expand the $$e^{-Kt}$$ out but I want to confirm. In that case can i say that...

I have two questions about the use of stochastic differential equation and probability density function in physics, especially in statistical mechanics. a) I wonder if stochastic differential equation and PDF is an approximation to the actual random process or is it a law like Newton's second...

A question for those who are computational physicist: Dear Computational physicist, I am struggling between computational physics course or numerical analysis. They are both in graduate level (so very intensive), one in physics department and another in math. Both are taught by leading experts...

In Griffith and Sakurai QM book, spontaneous emission is treated as a closed system subject to time-dependent perturbation. Yet in quantum optics sponantanoues emission is treated as in the form master equation of density matrix. Even in two levels system where there is only one spontaneous...

RIP

Which theoretical physicists win nobel prize based on their works in 30s or 40s?

They are being 2 by 2 matrices and I being the identity. Physically they are Pauli matrices. 1. Is $$((A\otimes I\otimes I) + (I\otimes A\otimes I) + (I\otimes I\otimes A))\otimes B$$ = $$(A\otimes I\otimes I)\otimes B + (I\otimes A\otimes I)\otimes B + (I\otimes I\otimes A)\otimes B$$? I...

System is composed of two qubits and the bath is one bath qubit. The interaction Hamiltonian is: $$\sigma_1^x\otimes B_1 + \sigma_2^x\otimes B_2$$ where $$B_i$$ is a 2 by 2 matrix. I try to interpret and understand this, is it the same as: $$(\sigma_1^x\otimes B_1)\otimes I_2 +...

Which course/book introduce asymptotic notation a deep and rigorious level, yet assume students did not know asymptotic notation before. It should nvolve proof of big O notation like superpolynomial and subexponenial.

Why is $$ \left(x^2-1\right)\frac{d}{dx}\left(x^2-1\right)^n = 2nx\left(x^2-1\right)^{n-1} $$? This is in a textbook and says that its proof is left as an exercise. It seems to be a difficult equality. I believe this should just be $$ \left(x^2-1\right)\frac{d}{dx}\left(x^2-1\right)^n =...

$$ \frac{d^{2n}}{dx^{2n}}\left(x^2-1\right)^n = (2n)! $$

I also wonder if there is a neat expression for such vector?:oldsmile:

Thanks for the reply. But why is Gram Schmidt process needed? My original brute force idea is to solve n-1 equations.

Given n linearly independent vectors, v1, v2, v3, ...vn. How to find construct a vector that is orthogonal to v2, v3, ..., vn (all v but not v1)? Is Gram Schmitt process the way to do this? or just by brute force?