Homework Statement
Consider a particle, with mass m, charge q, moving in a uniform e-field with magnitude E and direction X_1.
The Hamiltonian is (where X, P, and X_1 are operators):
The initial expectation of position and momentum are <X(0)> = 0 and <P(0)>=0
Calculate the expectation...
Homework Statement
Consider the bipartite state:
|q> = a/sqrt (2) (|1_A 1_B> +|0_A 0_B>)+sqrt((1-a^2)/2) (|0_A 1_B>+|1_A 0_B>)
where a is between or equal to 0 and 1
a) compute the state of the subsystem p_b
b) compute the purity of p_b as a function of a
c) for what values of a is the...
Homework Statement
Consider the bipartite observable
O_AB = (sigma_A · n) ⊗ (sigma_B · m)
Where n and m are three vectors and
sigma_i = (sigma_1_i, sigma_2_i, sigma_3_i)
with i = [A,B] are the Pauli vectors.
Compute using abstract and matrix representation the expectation value of O_AB...
Homework Statement
Given a orthonormal basis of the hilbert space of qutrit states: H = span (|0>, |1>, |2>)
write in abstract notation and also a chosen consistent matrix representation, the states
a) An equiprobable quantum superposition of the three elements of the basis
b) An...
Homework Statement
Using the given equations prove that
Homework Equations
,
,[/B]
+
(it won't render together in Maple for whatever reason)
The Attempt at a Solution
So I started with expanding the Jacobi Identity (the third relevant equation) and through tedious algebra arrived...
Homework Statement
Use the formulas given (which have been solved in previous questions) prove that
where w_12 is a complex constant.
From here, induce that
where eps_abc is the fully anti-symmetric symbol
Homework Equations
The equations given to use are:
The Attempt at a...
Homework Statement
Prove that applying an infinitesimal rotation of angle k<<1 around the axis x1, then a boost of speed -k along the axis x2 then the inverses of these is equal to a single boost of speed k^2 along the axis x3
The Attempt at a Solution
Putting this into mathematical terms I...
Homework Statement
Show explicitly that
ei*ε*κu * ei*ε*κv * e-i*ε*κu* e-i*ε*κv = Identity + ε2 [Kv,Ku + O (ε3)
The Attempt at a Solution
Kv,Ku = Kv*Ku - Ku*Kv
I'm not sure exactly how to approach this problem. I know that
U (tau) = ∏ ei*su*Ku
and that for operators O --> O' = U O U†...
Homework Statement
The e-states of H^0 are
phi_1 = (1, 0, 0) , phi_2 = (0,1,0), phi_3 = (0,0,1) *all columns
with e-values E_1, E_2 and E_3 respectively.
Each are subject to the perturbation
H' = beta (0 1 0
1 0 1
0 1 0)
where beta is a positive constant...
Homework Statement
Consider the following inital states of the symmetric 2D harmonic oscillator
ket (phi 1) = 1/sqrt(2) (ket(0)_x ket(1)_y + ket (1)_x ket (0)_y)
ket (phi 2) = 1/sqrt(2) (ket(0)_x ket(0)_y + ket (1)_x ket (0)_y)
Calculate the <p_x (t)> for each state
Homework Equations
The...
Homework Statement
Are the following matrices hermitian, anti-hermitian or neither
a) x^2
b) x p = x (hbar/i) (d/dx)
Homework Equations
The Attempt at a Solution
For a) I assume it is hermitian because it is just x^2 and you can just move it to get from <f|x^2 g> to <f x^2|g> but I am...
Homework Statement
Look at the matrix:
A = sin t sin p s_x + sin t sin p s_y +cos t s_z
where s_i are the pauli matrices
a) Find the eigenvalues and normalized eigenvectors (are they orthogonal)?
b) Write the eigenvector of s_x with positive eigenvalue as a linear combination of the...
Homework Statement
This is a standard projectile motion problem, the mass is m, the drag is F_r = - alpha *v, where alpha is a positive retarding coefficient. The origin is the ground and at time t = 0 the horizontal and vertical velocities are positive
a) Write down Newton's second law for...
Homework Statement
Find the mutual inductance between a coil with N loops and an infinite straight line with current I on its axis.
Homework Equations
M12 = M21 = flux 1/I 2 = flux 2/ I 1
emf = -d/dt flux
i = emf /R
R = eta*l/S
The Attempt at a Solution
I have done this...
Homework Statement
A circular coil has N equal loops with diameter C. Each loop has resistivity η and diameter d.
There is a field on the central axis of B(t) = B_0 sin(ωt).
Find the induced current (ignoring other fields)
Homework Equations
emf = -d/dt * flux(t)
i = emf/R
R = η*l/A...
Homework Statement
The e-functions for n=0,1,2 e-energies are given as
psi_0 = 1/(pi^1/4 * x0^1/2)*e^(x^2/(2*x0^2)
psi_1 =...
psi_2 =...
The factor x0 is instantaneously changed to y= x0/2. This means the initial wavefunction does not change.
Find the expansions coefficients of the...
Homework Statement
I am given a set of x and y values x: (1,2,3,etc.) y: (1.2,2.2,3.1,etc.) with a given uncertainty and am asked
a) find the best fit
b) at what prob can you rule out a 5% higher slope
c) is the stated uncertainty consistent with the data?
Homework Equations...
Homework Statement
So I am calculating the error for something and I am getting really weird values.
So I know that the value for the Inductor is 24.97 +- 0.005 mH and that for the capacitor is 105.7+-0.0005 nf.
So I am finding the value for the resonant frequency
Homework Equations...
Homework Statement
Use a coordinate conversion application to roughly map out the amount of precession in coordinate
positions (R.A and Declination) in the sky between 1950 and 2000.
Homework Equations
I can easily find a converter on the internet
The Attempt at a Solution
I...
Homework Statement
Calculate the torque, t about origin that must be applied to a particle for it to maintain a constant speed v along a cardiod.
Homework Equations
t = r x f
a = (r_dot dot - r*Θ_dot ^2) r_hat + (r*Θ_dot dot + 2 r_dot * theta_dot) theta_hat
The Attempt at a...
Homework Statement
A particle moves with const speed v along the curve r(θ) = a(1+cos θ).
Starting with the general expression for the velocity vector v in polar coordinates solve for θ_dot in terms of v, k, and θ. What does the sign of θ_dot signify?
Homework Equations
v = r_dot*r_hat +...
Homework Statement
How much time does it take a planet with surface temperature of 100K and a radius of 500 km to cool down to 50K, ignoring solar heating. Assume E_thermal = 3/2 NkT and that the surface radiates as a blackbody. Calculate this by using the relationship between thermal energy...
Homework Statement
What is the flux on a solar sail per square meter, if it orbits the Sun at 3 AU. Flux at 1 AU is 1.36 KW/square meter
Homework Equations
Flux goes as 1/r^2
The Attempt at a Solution
Flux at 3 AU will be 1.36/3^2 = 1.36/9 = 0.15 KW/square meter
I can't...
Homework Statement
Find Kirchoff's laws for this
http://postimg.org/image/d78dvdg5f/
(Actual problem has a bit more but I can do that part.)
Homework Equations
Loop rule
Junction rule
The Attempt at a Solution
I got the following equations
2e - 4i_4 - 2i_2 = 0
e - 3i_3 - i_1 = 0
e -...