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  1. M

    Expectation of position and momentum at time t, pictures

    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...
  2. M

    Bipartite state purity

    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...
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    Expectation value of observable in Bell State

    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...
  4. M

    Superposition of Hilbert space of qutrit states

    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...
  5. M

    Show that [J_a,G_a] = 0, commutation relationships

    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...
  6. M

    Prove commutation relation of galilei boosts and rotations

    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...
  7. M

    Show that rotations and boosts lead to a combined boost

    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...
  8. M

    Galiliei transformations explicit proof

    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†...
  9. M

    Perturbation Hamiltonian

    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...
  10. M

    Expectation value of momentum in symmetric 2D H.O

    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...
  11. M

    Are the matrices Hermitian?

    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...
  12. M

    Eigenvalues and eigenvectors, pauli matrices

    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...
  13. M

    Projectile motion with air resistance

    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...
  14. M

    Mutual inductance coil line

    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...
  15. M

    Induced current from coil

    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...
  16. M

    Modified Harmonic Oscillator probabilities

    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...
  17. M

    Is the uncertainty consistent?

    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...
  18. M

    Error Propagation dividing

    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...
  19. M

    Astronomy; Precession data co-ordinate systems

    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...
  20. M

    Acceleration at constant velocity?

    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...
  21. M

    Polar coordinates theta

    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 +...
  22. M

    Planterary Cooling

    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...
  23. M

    Find force from flux

    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...
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    Kirchhoff rules

    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 -...
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