All Questions
Tagged with physics special-functions
31
questions
0
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22
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SixJSymbol not triangular in basis transformation
The basis transformation is given by
$$\left| J^{P}, jd \right\rangle = \sum_ {S} (-1)^{J + L + Sd + Sq}\sqrt {(2 S + 1) (2 jd + 1)}\, \biggl\{\begin {array} {ccc} L & Sq & J \\ S & Sd &...
0
votes
0
answers
60
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Clebsch–Gordan coefficient calculation for L-S basis in system of three particles
I am trying to calculate eq (A3)
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0
votes
1
answer
84
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Evaluate the time average of Mathieu functions
I defined a function composed of Mathieu's periodic functions:
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1
vote
0
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25
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Finding the coefficients of a decomposition of complicated expression into products of special functions
I have the following expression which arises while studying minimal models in CFT. The 4-point amplitude of scalars is given by
$$G(z,\overline{z}) = ((1-z)(1-\overline{z}))^{\frac{m-1}{m+1}}\mathcal{...
- 411
2
votes
2
answers
240
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Can the CopulaDistributions be fitted?
This is an immediate follow-up to DoAny--which I did consider editing, clarifying and correcting in some respects.
But perhaps here I can put the immediate question at hand more directly (the emphasis ...
- 2,335
0
votes
1
answer
137
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Expectation Value of a Potential Using Radial Solution of Hydrogen Atom
I am trying to input $R_{nl}$, which is the radial solution of the hydrogen atom and I would like to obtain an expectation value of particular potential. This is my code:
...
2
votes
1
answer
102
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Clebsch-Gordan coefficients: General Expression Does Not Match Specific Expression
The expression ClebschGordan[{2, 0}, {4, 0}, {2, 0}] yields the correct result of Sqrt[2/7].
However the expression ...
- 33
4
votes
1
answer
295
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Evaluating a hard integral related to the two-fluid model
The following definite integral describing the density of the normal part of a superfluid equals to
$$
\int_0^\infty dx\, x^4\, \frac{e^{x^2+a}}{\left(e^{x^2+a}-1\right)^2} = \frac{3\sqrt{\pi}}{8}Li_{...
- 143
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1k
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Radial wave-function integration with mathematica
I'm new in using Mathematica. I wanted to do some integrations with the radial wave function for Hydrogen atom. The radial wave function is given by,
$$R_{nl}(r)=2^{l+1} e^{-\frac{r}{a n}} \sqrt{\frac{...
- 101
9
votes
2
answers
2k
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The time-like geodesics (orbits) in the Schwarzschild spacetime
I am trying to plot Schwarzschild's orbit without invoking the geodesic equation.
As a reference I am using Chandrasekhar's Book (The Mathematical theory of Black Holes, Oxford University Press). In ...
- 196
1
vote
0
answers
57
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How to solve an Integral analytically using a predefined definition for Besselfunctions (phi part of angular spectrum representation)
I'd like to use mathematica to calculate an Integral that is dependent on phi and theta (to obtain the intensity distribution of a tightly focused TEM20 mode using the angular spectrum representation)....
- 21
4
votes
1
answer
1k
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Plot of Laguerre-Gaussian wavefront
I have tried to plot the wavefront of a Laguerre-Gaussian beam, I know that to do that I have to plot the set of all points where the wave has the same phase.
I have try to use the conditional ...
0
votes
0
answers
541
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Clebsch Gordan coefficients
I'm trying to compute various sums which contain some CG coefficients, where the sum runs over the indexes m1,m2,m corresponding to each of the three angular momenta j1,j2,j. The thing is that when I ...
- 109
9
votes
1
answer
1k
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Definition of WignerD function?
On Wikipedia, elements of Wigner's D-matrix are defined as
$$D_{m'm}^{j}(\alpha,\beta,\gamma)=\langle jm'|e^{-i\alpha J_z}e^{-i\beta J_y}e^{-i\gamma J_z}|jm\rangle=e^{-im'\alpha}d_{m'm}^j (\beta)e^{-...
- 263
5
votes
1
answer
463
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HypExp and HPL packages for hypergeometric functions: Evaluating a function HPL[{minus,plus},x]?
I am currently using the HypExp and HPL packages, which are useful for expanding hypergeometric functions in series around integer or half-integer values, as in common in dimensional regularization ...
- 183