# Tagged Questions

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### Really could use some advice with this PDE [on hold]

so I'm faced with a partial differential equation that I have been able to solve only in one limiting case. I have asked the mathematics stack exchange twice for literally any help whatsoever to no ...
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### Is the algebra of a differential equation invariant under transformation?

I've found that the algebra of this differential equation $$\frac{d^2y}{dz^2}-(3z^2+\gamma)\frac{dy}{dz}+(cz+\alpha)y=0$$ is in $sl(2)$ because it is possible to use the generators of the $sl(2)$ ...
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### Solution of QM tasks by using asymptotics

When we solve QM tasks by solving Schrodinger equation, such as tasks about particle in Morse potential, Poschl-Teller potential and many others, we usually find an approximations (lets call them as ...
I am interested in the link between the Black & Scholes equation and quantum mechanics. I start from the Black & Scholes PDE $$\frac{\partial C}{\partial t} = -\frac{1}{2}\sigma^2 S^2 ... 3answers 279 views ### Bessel vs. modified Bessel in radial equation of hydrogen I am trying to understand the difference between Bessel functions and modified Bessel functions (simply googling is yielding complicated, non-intuitive answers). I was under the impression that one ... 3answers 251 views ### How do I integrate \frac{1}{\Psi}\frac{\partial \Psi}{\partial x} = Cx How do I integrate the following?$$\frac{1}{\Psi}\frac{\partial \Psi}{\partial x} = Cx where $C$ is a constant. I'm supposed to get a Gaussian function out of the above by integrating but don't ...
As students on solid state physics, we are all taught to use the periodic boundary condition, taking 1D as an example: $\psi(x)=\psi(x+L)$ where $L$ is the length of the 1D crystal. My question is: ...