but the equation only uses the vector R, not phi or theta. e is only a function of r, so wouldnt it be like saying take the derivative of this function w.r.t. r, then take the derivative of a constant with respect to theta, then the derivative of a constant with respect to phi?
Homework Statement
Show that \epsilon(r)=\frac{A}{r}e^{ikr} is a solution to \nabla^{2}\epsilon(r)+k^{2}\epsilon(r)=0
Homework Equations
The Attempt at a Solution
Is \nabla^{2} in this case equal to \frac{\partial^2}{\partial r^2} or \frac{\partial^2}{\partial...
Homework Statement
A filter is used to obtain approximately monochromatic light from a white sources. If the pass band of the filter is 10 nm, what is the coherence length and coherence time of the filtered light? The mean wavelength is 600 nm.
Homework Equations
c\tau_{0}=l_{c}...
Homework Statement
Suppose the number density of bright F dwarf stars at the Sun's radial distance from the Galactic center, varied with height above the galactic plane as:
n(z)=n0 exp(-z/h)
where h = 250 pc. Also suppose that the velocity dispersion of these dwarfs varies with z as...
Homework Statement
A stromgren sphere is the sphere surrounding a star where the photons from the star can ionize the gas. So the radius of the sphere is the extent from the star in which the gas is ionized. For a fully ionized (idealized, for this question) sphere of gas, the number of...
okay, i used mathematica, i created functions for each term, did all the necessary derivatives and additions, and what i got was
(2 a^2 e^2 m - 8 a h^2 pi epsilon + h^2 pi r epsilon)/(8 a^2 m pi r epsilon)
this answer was close with the exception of r, everything else is a constant
okay, but quick question first
\frac{d}{dr}(r^2\frac{d}{ dr})
is this line asking you to take the derivative of R, multiply it by r^2, and then take the derivative of the resulting equation?
What does it mean to "satisfy" the Schrodinger equation?
Homework Statement
Show that the 2p wave functions of the hydrogen atom satisfy the radial Schrodinger eq.
One of the radial equations for the 2p state is \frac{1}{\sqrt{96 \pi a^{3}}} \frac{r}{a} e^{\frac{-r}{2a}}
Homework Equations...
As the equation is right now, it has no theta or phi terms. Wouldnt I have to know the quantum numbers n, l, and m in order to introduce the other terms?
Homework Statement
Starting with \psi(r,\theta,\phi)=R(r)Y(\theta,\phi) saubstitute into the Schrodinger equation and show (using the technique of separation of variables) that R satisfies:
(\frac{\hbar^2}{2m}\frac{1}{r^2}\frac{d}{dr}(r^2\frac{d}{dr})+\frac{C}{2mr^2}+V(r))R=ER(r)
Homework...
Homework Statement
I have a test in my physics class on tuesday, and as a study guide, our professor gave us a sample test and the solutions. I worked through most of it, except for this one question. I don't understand his method to solving it, I was hoping you guys had a solution. I have...
Homework Statement
Suppose one photon has an energy of 200 MeV and it is traveling along the x-axis. Suppose another has an energy of 100 MeV and is traveling along the y-axis. (A) What is the total energy of this system. (The answer is 300 MeV) (B)If a single particle has this same...
Homework Statement
A particle is observed in a certain reference frame (i.e. observer A) has a total energy of 5GeV and a momentum of 3GeV/c.
(a) What is the energy of the frame in which its momentum is equal to 4GeV/c.
Homework Equations
E'={\gamma}E-{\gamma}{\beta}(cp)...
Homework Statement
The velocity of a proton relative to
our galaxy is vp/c = 1-(0.5*10^20), i.e. almost one. Such protons are actually observed.
When velocity it very nearly one \gamma is very large. 1/\gamma
is very small. Use Taylor series to show that for v almost one we have...