Now w/ Attachment: Telephone Wire w/ Load and Characteristic Impedance
Homework Statement
Please see attachment.
Homework Equations
I(z)=I+(exp(-γz)) + I-(exp(γz))
V(z)=V+(exp(-γz)) + V-(exp(γz))
The Attempt at a Solution
I solved easily for the characteristic impedance and gamma...
Homework Statement
Evaluate the matrix element <U210|z|U100> where by |Unlm> we mean the hydrogen atom orbital with it's quantum numbers.
Homework Equations
The Attempt at a Solution
So where I'm getting stuck is on the integral, because the "U" portion of the wave function is...
Or perhaps the method I chose isn't even close...if so could someone please just give me a hint on a better method? I don't know if what I'm doing is just creating a bunch of smoke, or if it's on the correct path. I've been struggling with this problem for days!
Homework Statement
Consider the energy surface
E(k)=h2((kx2 +ky2 )/ml+kz2/mt
where m_l is the transverse mass parameter and m_l is the longitudinal mass parameter. Use the equation of motion:
h(dk/dt)= -e(vXB) with v=∇k(E)/h to show that ωc=eB/(ml*mt)1/2 when the static magnetic field B...
So would the only thing that really matters be the exp(+/-(E3-E1)it/h), where ω=(E3-E1)/h? It just seems strange to me that whether one eigenstate dominates or not does not affect the frequency of electron probability density.
Also, I have difficulty in general with normalization. If I...
Homework Statement
An electron in an infinitely deep potential well of thickness 4 angstroms is placed in a linear superposition of the first and third states. What is the frequency of oscillation of the electron probability density?
Homework Equations
E=hω
The Attempt at a Solution
My...
So I am assuming to find a1 I simply perform <δ1|ω1>, and I would get a1=i/sqrt(3), and similarly a2=sqrt(2/3), a3=0, and then I could put |ω1> into column form:
(a1)
(a2)
(a3)
(that is my attempt at a column matrix).
I could do a similar thing for |ω2> to get coefficients b1=(1+i)/sqrt(3)...
Homework Statement
Note: I am going to use |a> <a| to denote ket and bra vectors
The components of the state of a system| ω1> in some basis |δ1>, |δ2>, |δ3> are given by
<δ1|ω1> = i/sqrt(3), <δ2|ω1> = sqrt(2/3), <δ3|ω1> = 0
Find the probability of finding the system in the state |ω2>...
The problem I run into is when I do this I can't get the x^2 terms to cancel (and I thought eigenenergies had to be constant).
so for the first term, θ1:
1/(pi)^1/4*(-0.5h^2(d/dx)^2*(exp(-x^2/2)) + 0.5x^2(exp(-x^2/2)))
=1/(4*pi)^1/4[-h^2*(exp(-x^2/2)(x^2-1) + x^2(exp(-x^2/2))]
Now...
Thanks for your response! I wanted to clarify what you mean by also replacing θ1(x) by its normalized form. Do you mean including the exponential function that is dependent on x? So that:
ψ(x,0)= 1/sqrt(8*pi) θ1(x) + 1/sqrt(18pi) θ2(x)
becomes...
Homework Statement
Consider the Hamiltonian H=0.5p^2+ 0.5x^2, which at t=0 is described by:
ψ(x,0)= 1/sqrt(8*pi) θ1(x) + 1/sqrt(18pi) θ2(x), where:
θ1= exp(-x^2/2); θ2=(1-2x^2)*exp(-x^2/2)
a) Normalize the eigenfunctions and rewrite the initial state in terms of normalized...
I thought about an induction proof-- I have some experience with these, but evidently not that much. After I get to where I left off:
(x,p^n)=(x,p*p^(n-1)=(x,p)p^(n-1)+p(x,p^(n-1))=ip^(n-1) + p(x,p^(n-1))
I have to somehow turn this into ixp(n-1). I can't figure out how to get an "x" in...
Homework Statement
Using (x,p) = i (where x and p are operators and the parentheses around these operators signal a commutator), show that:
a)(x^2,p)=2ix AND (x,p^2)=2ip
b) (x,p^n)= ixp^(n-1), using your previous result
c)evaluate (e^ix,p)
Homework Equations
For operators, in...
Homework Statement
In the case of an electron wave packet, the function A(k) has a rectangular shape, i.e. it is equal to A0 if k0-a<k<k0+a, and zero everywhere else. (a) Find the minimal uncertainty of electron position. (b) Find the electron wavefunction.
Homework Equations
ΔxΔp=h/4pi...
1. Homework Statement
Two semi-infinite grounded conductive planes meet at right angles. In the region b/w the conductors, there is the plane with angle 45° having surface charge density σ. Using the method of images, find the field distribution in this region.
(There is a picture included...