from that distribution we get $$ \left(3a_{+}\psi_{0}\left(x\right)e^{-\frac{i\omega t}{2}}+4a_{-}\psi_{1}\left(x\right)e^{-\frac{3i\omega t}{2}}+3a_{-}\psi_{0}e^{-\frac{i\omega t}{2}}+4a_{-}\psi\left(x\right)e^{-\frac{3i\omega t}{2}}\right)$$
and
$$a_{+}=\sqrt{n+1}\psi_{n+1}...
In part C. I need to find $$\left<x\right>$$ and $$\left<p\right>$$ using Ladder Operators:
$$\Psi\left(x,t\right) = \frac{1}{5}\left(3\psi_{0}\left(x\right)e^{-\frac{i\omega t}{2}}+4\psi_{1}\left(x\right)e^{-\frac{3i\omega t}{2}}\right)$$
$$x =...
However, I just found the equation
E_(n) = (n+1/2)ħω
so it makes sense now, however, I have a question about part C. which is find <x> and <p>.
so x = (ħ/(2mω))^(½)(a_(+)-a_(-)) and <x> = (1/25)(ħ/(2mω))^(½)(∫Ψ^*(a_+a_-)Ψdx but I am alittle confused on what to do next.
I believe what happens...
The full problem is:
A particle in the harmonic oscillator potential starts out in the state Ψ(x,0) = A[3ψ_0(x)+4ψ_1(x)]
A. = Find A, A = 1/5
B. Construct Ψ(x,t) and |Ψ(x,t)|^2:
Ψ(x,t) = 1/5[3ψ(x)e^(-((iE_0 t)/ħ)+4ψ(x)e^(-(iE_1 t)/ħ)]
What I understand is that the the harmonic states is 0 and...
Homework Statement
construct ψ(x,t)^(2) where ψ(x,t) = 1/5(3ψ_0(x)e^(-iE_0t/ħ)+4ψ_1(x)e^(-iE_1t/ħ). I know we square it but we have to find E_0 and E_1 and put it in.
Homework Equations
E_n = (ħ^(2)k_n^(2))/2m = (n^(2)π^(2)ħ^(2))/2ma^(2)
The Attempt at a Solution
E_0 = 0 and E_(1) =...
Homework Statement
An A.H. Pfinds's method for measuring the index of refraction of glass is illustrated in the figure. One face of a slab of thickness t is painted white, and a small hole scraped cleat at point P serves as a source of diverging rays when the slab is illuminated from below...
Homework Statement
The walls of an ancient shringe are perpendicular to the four cardinal compass directions. On the first day of spring, light from the rising sun enters a rectangular windows in the eastern wall. The light traverses 2.37m horizontally to shine perpendicularly on the wall...
Yeah I used the three variable Pythagorean Theorem and than took the derivative and than placed values for x and y so I could graph it.
Here's the typed worksheet: https://dl.dropbox.com/u/77575413/F.pdf [Broken]
on the second page I have the graphs of Time and the derivative of Time and as...
Hi, I am trying to prove the second law of reflection using fermat's principle and I am not entirely sure how to start it.
By the way the second law of reflection is: The incident ray, reflect ray and normal ray all lie in a single plane.
Hi,
I am working on my notes dealing with standing waves and I was wondering would a graph of the equaion y(x,t)= 2Acos(ωt)sin(kx) just a regular wave? Also I was wondering why are standing waves called standing waves. Im sorry if this is the wrong forum.