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I am a PhD student in Physics that studies math as a hobby.

My current mathematical interests involve p-adic and adelic numbers and in particular their applications to alternative formulations of quantum mechanics that do not have a "preferred" number system.

My favorite mathematical proof is Euler's solution of the Basel problem using the infinite product representation of the sinc function.


22h
comment Fourier Series in different forms
It would be helpful if you shared some details of how you computed the coefficients. For instance how did you compute the constant terms? Since these only involve integrating your function over the interval I am mystified that you got a different result in both cases.
Sep
11
comment Vector functions in engineering
"Engineering" covers a lot of different disciplines. Could you narrow that down a bit?
Sep
10
comment Curl and divergence of vector fields
It sounds like you are studying physics in which case we don't really care if the field is defined at that point. The definition for divergence that you gave also doesn't care since its only the limit as the volume shrinks down to the point.
Sep
8
answered Definition of Bilinear maps.
Sep
8
comment Integration of gaussian times absolute value of cosine
@coolydudey60, Do you mean how do we evaluate the integral with a $\cos^2(x)$? This can be done by replacing $\cos(x)=(\exp(ix)+\exp(-ix))/2$ and then completing the square in the exponents. Then its no harder than evaluating a normal gaussian integral.
Sep
8
comment Integration of gaussian times absolute value of cosine
Only thing I can think of at the moment is that $\cos^2(x) \leq \left| \cos(x) \right| $ which could give you a decent lower bound on the integral.
Jul
7
reviewed Leave Open Integer values of $\frac{x}{y}+\frac{y}{z}+\frac{z}{x}$?
Jul
7
comment show that the Taylor series of $f (x) = e ^{-1 / x ^ 2}$ around $x_0 = 0$ is identically zero
@Gina, the taylor series certainly doesn't converge to the function, but that is different from saying it doesn't exist.
Jul
7
comment show that the Taylor series of $f (x) = e ^{-1 / x ^ 2}$ around $x_0 = 0$ is identically zero
I think it is pretty clear that the singularity is removable. After all we are talking about the Taylor series of $\exp(-1/x^2)$ about the point $x=0$, which is the only point at which the function doesn't even exist if we take it too literally. Is there something more subtle that I am missing here?
Jul
7
comment How to solve $\sin^3 x=\sin x\,$?
I'm going to second David here. You're previous question is basically the same as this one. If you can solve that you should have no problem solving this.
Jul
7
comment Integral with Dirac Delta
Cool, I'll take a crack at it when I have some time.
Jul
5
comment Integral with Dirac Delta
It would be helpful to know what can we assume about $\Psi$ and the range of integration. For instance in these situations integration by parts usually gets used quite liberally, but that only makes sense if $\Psi$ is zero on the boundary of our region.
Jul
5
comment Integral with Dirac Delta
Its not entirely clear to me what the exact nature of the rest of your question is. Are you trying to show that the integral simplifies to "$\hat{H} = \frac{1}{4}g_2\int d^3R\ \bar{\Psi}(\vec{R})\left[ \nabla^2(\bar{\Psi}(\vec{R})\ \Psi(\vec{R}))\right]\Psi(\vec{R})$"?
Jul
5
comment Integral with Dirac Delta
This was meant to answer to the first question you listed: "Using dirac delta properties, can i say that $\left[ \delta(\vec{r} )\nabla^2_{\vec{r}} +\nabla^2_{\vec{r}}\delta(\vec{r}) \right]=2\delta(\vec{r})\nabla^2_{\vec{r}} $?".
Jul
4
answered Integral with Dirac Delta
Jul
4
comment Derivatives in the real world
The equation you're having trouble with is called the law of cosines. Its like the pythagorean theorem but more general.
Jul
3
reviewed Leave Open Completion of a torsion-free module
Jun
30
reviewed Approve suggested edit on If $ x^2+y^2+z^2 =1$ for $x,y,z \in \mathbb{R}$, then find maximum value of $ x^3+y^3+z^3-3xyz $.
Jun
30
reviewed Reopen Maximum Likelihood Estimator for a Poisson random variable
Jun
30
revised Interesting dilemma, answer not matching with stewart, My work is Included
deleted 13 characters in body