# Search results

1. ### Telephone Wire with Load and Characteristic Impedance

Sorry, now the problem is attached.
2. ### Telephone Wire with Load and Characteristic Impedance

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...
3. ### Hydrogen Atom Matrix Elements Related to Transition Probability

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...
4. ### Finding ω_c Given an Energy Surface E(k) in Constant Magnetic Field

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!
5. ### Finding ω_c Given an Energy Surface E(k) in Constant Magnetic Field

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...
6. ### Normalization of Linear Superposition of ψ States

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...
7. ### Normalization of Linear Superposition of ψ States

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...
8. ### Probability of Finding System in a State Given a Particular Basis

Much clearer now...I appreciate you clearing that up for me!
9. ### Probability of Finding System in a State Given a Particular Basis

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)...
10. ### Probability of Finding System in a State Given a Particular Basis

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>...
11. ### Rewriting an Initial State with Normalized Eigenfunctions

Yes, makes sense, thank you!
12. ### Rewriting an Initial State with Normalized Eigenfunctions

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...
13. ### Rewriting an Initial State with Normalized Eigenfunctions

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...
14. ### Rewriting an Initial State with Normalized Eigenfunctions

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...
15. ### Commutator Proof: Show (x,p^n)= ixp^(n-1)

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...
16. ### Commutator Proof: Show (x,p^n)= ixp^(n-1)

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...
17. ### Minimum Uncertainty in Electron Position: Rectangular Wave in k-space

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...
18. ### Calculating Field by Method of Images due to Plane Wedged b/w Grounded Conductors

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...