Hello everyone. I am currently using the pca function from matlab on a gaussian process. Matlab's pca offers three results. Coeff, Score and Latent. Latent are the eigenvalues of the covariance matrix, Coeff are the eigenvectors of said matrix and Score are the representation of the original...
I started with the first of the relevant equations, replacing the p with the operator -iħ∇ and expanding the squared term to yield:
H = (-ħ^2 / 2m)∇^2 + (iqħ/m)A·∇ + (q^2 / 2m)A^2 + qV
But since A = (1/2)B x r
(iqħ/m)A·∇ = (iqħ / 2m)(r x ∇)·B = -(q / 2m)L·B = -(qB_0 / 2m)L_z
and A^2 =...
1. Homework Statement
Consider a potential field
$$V(r)=\begin{cases}\infty, &x\in(-\infty,0]\\\frac{\hslash^2}{m}\Omega\delta(x-a), &x\in(0,\infty)\end{cases}$$
The eigenfunction of the wave function in this field suffices...
Consider a potential cavity
$$V(r)=\begin{cases}\infty, &x\in(-\infty,0]\\\frac{\hslash^2}{m}\Omega\delta(x-a), &x\in(0,\infty)\end{cases}$$
The eigenfunction of the wave function in this field suffices
$$-\frac{\hslash^2}{2m}\frac{d^2\psi}{dx^2}+\frac{\hslash^2}{m}\Omega\delta(x-a)\psi=E\psi$$...
Hi at all,
I'm tring to solve Schrodinger equation in spherically simmetry with these bondary conditions:
##\lim_{r \rightarrow 0} u(r)\ltimes r^{l+1}##
##\lim_{r \rightarrow 0} u'(r)\ltimes (l+1)r^{l}##
For eigenvalues, the text I'm following says that I have to consider that the...
Hey,
I have a question concerning eigenfrequencies:
Let us assume we examine a beam that is fixed at one end and free at the other end. It is possible to get an analytical solution in form of a unlimtied series: sum_i=1..infinity eigenfunction(i)*exp(i*eigenfrequencie(i)*t). (something...
Hi everyone,
I have some knowledge of Hilbert spaces and Functional Analysis and I have the following question.
I ofter have read that "Fourier transform diagonalize the convolution operator". So, we can say that for LTI systems (that can always be described with a convolution and "live" in...