I have this Hamiltonian --> (http://imgur.com/a/lpxCz)
Where each G is a matrix.
I want to find the eigenvalues but I'm getting hung up on the fact that there are 6 indices. Each G matrix lives in a different space so I can't just multiply the G matrices together. If I built this Hamiltonain...
1. Homework Statement
Here is the problem: http://imgur.com/XEqE4SY
2. Homework Equations
|psi_s_ms> = |s, ms> ⊗ Σ D_i_j |psi_i, psi_j>
3. The Attempt at a Solution
I know the singlet state in the |s, ms> basis is |0,0> = (1/sqrt(2))[ |up, down> - |down, up>] and that the hamiltonian for...
1. Homework Statement
Question: http://imgur.com/YzexPKl (only part c)
2. Homework Equations
From part a) I got |psi> = (1/sqrt(2))(e^(iwt/2)|z-up> + ie^(-iwt/2)|z-down>
I expanded this wave function in the x-spin basis and got,
|psi> = (1/(2))[(e^(iwt/2)+ie^(-iwt/2))|x-up> +...
say we have some wavefunction |psi> and we want to find the probability of this wavefunction being in the state |q>. I get that the probability is given by P = |<q|psi>|^2 since we're projecting the wavefunction onto the basis state |q> then squaring it to give the probability density.
However...
"Any number such that a given matrix minus that number times the identity matrix has a zero determinant."
I don't see how this answers the question. should non-integer multiples of ћ be omitted or not?
Say I apply a raising operator to the spin state |2,-1>, then by using the the equation
S+|s,ms> = ћ*sqrt(s(s+1) - ms(ms+1))|s,ms+1>
I get,
S+|2,-1> = sqrt(6)ћ|2,0>
Does this correspond to a physical eigenvalue or should I disregard it and only take states with integer multiples of ћ as...
Thanks for the reply!
but the whole reason we need to figure out < x | Px | x' > in the first place is because the identity operator is inserted. What's the point?
Also how to do you do this derivation step by step? I'm very confused I think my prof. is skipping steps
: http://imgur.com/tl07k5g
Image: http://imgur.com/pynKr8q
How is the boxed equation arrived at when looking at the step before?
I think I need clarification on a few key ideas:
in words, does < x | p | ψ > mean, "The momentum operator acting on the state vector, then projected onto the position basis"? If so, wouldn't...
How do you know when to use exponentials and trig functions when solving for the wave function in a finite square well? I know you can do both, but is there some way to tell before hand which method will make the problem easier? Does it have something to do with parity?
How can you tell if a given wave function isn't an eigenstate of the hamiltonian? I just don't get how if |Ψn(x, y)|^2 = |Anψn(x)e^-iEnt/h-bar|^22 and Ψ is a pure state, how doesn't the exponential factor cancel out in 1 = ∫ |Ψn(x, y)|2 dx ?
Here's the question: http://imgur.com/N60qRmw
I normalized the wave function and got A = sqrt(315/8L^9)
but how would I plot representative snapshots if the exponential factor will cancel when I square it? It's not a mixed state so it shouldn't depend on time as far as I can tell. Should I use...
1. Homework Statement
dNa/dt = -Na/Ta where Na is the function and Ta is the constant
dNb/dt = Na/Ta - Nb/Tb where Nb is the function and Tb is the constant
2. Homework Equations
My Prof said Nb(t) has the form Nb(t) = Cexp(-t/Ta) + Dexp(-t/Tb)
3. The Attempt at a Solution
I know the first...
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Thanks for the replies, it was just a simple separation of variables problem. It's strange how you sometimes forget the basics as your knowledge grows.
1. Homework Statement
y3(dy/dx) = (y4 + 1)cosx
2. The attempt at a solution
I solved for the homogeneous equation which is y = Ce-sinx Where C is some constant
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How...
Thank you I'll try it. I'm wondering if it would be more beneficial/ shed more light if I plotted x as a function of time. In that case I solved lagrange
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I would then need to solve...
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Here's some of my code: For simplicity, I assume period T(E) = 1
%Define Functions
%For a,b = 1
%U = ax^2 + bx^3
%Assuming T(E) = 1
U = @(x)...
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