Stationary States: Definition & Free Particle Incident

Sirius24
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Homework Statement



dJ(x,t)/dx = -dY^2 / dt , where y is the wave equation, and the d's represent partial derivatives. I want to make an assumption that I can describe the wave equation as a stationary state, so my question is the following:

What is the definition of a stationary state and can it be used to describe a free particle incident on a finite potential step from the left? This is not a specific question for the problem, but I need to know in order to make an assumption to solve it.
 
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I'm not that clued up on this myself, but stationary states appear to be similar to solving for standing waves on a string.

The assumption is made that the wavefunction y(x,t) = Bsin(kx +/- wt) (B arbitrary, k the wave number, w the angular frequency, x position and t time) and the wave is bouncing back and forth within a potential well "box". The stationary states correspond to the particular circumstances that produce standing wave patterns.
 
Hello everyone, I’m considering a point charge q that oscillates harmonically about the origin along the z-axis, e.g. $$z_{q}(t)= A\sin(wt)$$ In a strongly simplified / quasi-instantaneous approximation I ignore retardation and take the electric field at the position ##r=(x,y,z)## simply to be the “Coulomb field at the charge’s instantaneous position”: $$E(r,t)=\frac{q}{4\pi\varepsilon_{0}}\frac{r-r_{q}(t)}{||r-r_{q}(t)||^{3}}$$ with $$r_{q}(t)=(0,0,z_{q}(t))$$ (I’m aware this isn’t...
Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
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