# Questions tagged [differential-equations]

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### System PDE's non-linear [closed]

I am trying to solve the following system of PDE's. The idea behind this is that I have two media A,B and a collection of molecules. At medium A they can actively move at +x direction, whereas at ...
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### Solving Schrodinger equation for the hydrogen atom

In University Physics with Modern Physics by Hugh Freedman in Chapter 41.3 they go about solving the Schrodinger equation for the hydrogen atom. At one step they say to substitute the following ...
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### Dynamical system fixed point by perturbation?

Suppose I have an non-linear autonomous system : $$\dot{x}_i(t) = f(x_i(t)) + \lambda g(x_i(t))$$ I am interested in finding its fixed points. I want to know if the following method of ...
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### Is the linear combination of stationary states exhaustive? [duplicate]

After solving the Schrodinger Equation and getting the stationary states (separable solutions), we say the the general solution of the Schrodinger Equation is just the linear combination of these ...
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### Can't the heat equation be inverted?

I have heard people say that the heat equation isn't invertible because it smooths out irregularities that can not be recovered by backwards time evolution. But is this so? I will now argue that it ...
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### Differential equation [closed]

I am trying to solve the following differential equation; $$\frac{d^2 x}{d t^2}=-\omega^2 x \delta(t-t^\prime).$$ I know this is of the form $$x(t)= A \sin(\omega t) + B \cos(\omega t).$$ However this ...
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### David Hilbert's Prediction of Schrödinger Equation

In (Constance Reid 1996, Hilbert, p. 182): according to Condon: " ... when [Born and Heisenberg and the Gottingen theoretical physicists] first discovered matrix mechanics they were having, of ...
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### Cauchy problem of classical Maxwell equations in Minkowski spacetime

I'm wondering a bit about the classical Maxwell equations in flat spacetime and their Cauchy problem. For the following, I suppose that the sources are already given and don't react to their own ...
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### Angular Frequency of a charged particle moving in a Magnetic Field

I am trying to solve the Differential Equation in Mathematica but it is giving me error. How to find it's solution in Mathematica or in general. $$y'''=\frac{\omega^2E}{B}-\omega^2y'$$ The above ...
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### Looking for a good book on Differential Equations [duplicate]

I know many of you are tired of book recommendation posts and questions. But I am self learning Theoretical Physics, and I am having a hard time choosing a book to learn differential equations (ODEs). ...
44 views

### Derivation of MTZ Black Hole

I am trying to derive from scratch the MTZ Black Hole: https://arxiv.org/abs/hep-th/0406111 I have obtained equations (2.3) and (2.4) in terms of the metric functions and the scalar field. The metric ...
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### Uncertainty from variable to derivative in data fitting

If I have a system of differential equations, say $x' = f(x,p)$ and a set of data $(t_n,x_n)$, where $p$ is the set of constant parameters. I can then use a fitting method like least squared to obtain ...
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### Have water first order system dynamics or second order dynamics? [closed]

This is two transfer functions. One first order and the other is on second order $$G_1(s) = \frac{K}{1 + Ts}$$ $$G_2(s) = \frac{K\omega^2}{\omega^2 + 2\zeta \omega s + s^2}$$ The know characteristic ...
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### Solving the Lane-Emden equation via Chebyshev differentiation matrices

Problem So I'm trying to learn spectral methods but I can't quite proceed for some reason. In particular, I have been trying to solve the Lane-Emden equation (which I know how to solve via ...
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### “The state-space for a single particle in classical space is 6-dimensional” — Is this wrong?

The general argument is as follows. By Newton's second law $\mathbf F=m\ddot{\mathbf{x}}$. Now it is said that this is a second-order ODE and hence requires $\mathbf x(0)$ and $\mathbf{\dot{x}}(0)$ as ...
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### Solving a differential equation [closed]

($x$ here refers to position) $\frac{d^{2} x}{dt^{2}} + ω^{2}x$ = 0 After solving the above differential equation, we get $x(t) = Ae^{iωt} + Be^{−iωt}$ where $A$ and $B$ are some constants. My ...
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### How can a wave function that is both solution of classical wave equation and solution of Schrödinger equation be written?

Do wee need to solve the classical wave equation and Schrödinger equation together? Schrödinger equation has first time derivative while classical wave equation has the second time derivative. In ...
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### Formulations of the Einstein equations

The Einstein equations can be written as (here I am following the notation of Wald's book on General Relativity) \begin{equation} \partial_{\alpha}\Gamma^{\alpha}_{\mu\nu} - \partial_{\mu}\...
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### Physical interpretation of the heat equation with variable coefficient

I would want to know what is the physical interpretation of the heat equation with variable coefficients such that: $$u_{t}-\frac{1}{1+t^2}u_{xx}=0$$ well, I think I got it, it means that the ...
49 views

I have been trying to plot the variation of radial distance of a particle orbiting a Black Hole. The variation of radial distance from Black Hole is given by second order differential equation, $$\... 2answers 50 views ### Radioactive decay differential equations [closed] I am trying to form a differential equation between two different isotopes, Uranium-238 and Thorium-234. The rate of decay of an isotope is proportional to the amount present. So that:$$ \frac{dx}{...
Consider a small satellite of mass $m_0$ and initial velocity $v_0 >0$ that is far away from any external forces. It entered a dust cloud containing particles at rest that cling into the satellite'...