Consider the result of two consecutive rotation of a vector, first at the angle of 30 degrees then at the angle of 60 degrees. Do it first using multiplication of the respective matrices, and then by using a matrix representing a single rotation by angle of 90 degrees.
Consider linear transformation acting on a 3-d displacement vector, which reflects a vector with respect to its origin. Find a matrix T, which describes this transformation.
Show that eigenvectors of a unitary transformation belonging to distinct eigenvalues are orthogonal.
a) Show that eigenvalues of a unitary transformation have modulus 1. b) Show that eigenvectors of a unitary transformation belonging to distinct eigenvalues are orthogonal.
Consider lowering and rising operators that we encountered in the harmonic oscillator problem.
Consider lowering and rising operators that we encountered in the harmonic oscillator problem. 1. Show that a+ = 2. Find eigenvalues and eigenfunctions of the lowering operator 3. Does the rising operator have normalizable eigenfunctions?
Find the momentum-space wave function
Find the momentum-space wave function See attached file for full problem description.
The Hamiltonian of a certain three level system is represented by the matrix. See attached file for full problem description.
Eigen-Function. See attached file for full problem description.
Bohr Radius. See attached file for full problem description.
An X-ray photon of wavelength 6 pm (1 pm = 10^-12 m) makes a head-on collision with an electron, so that the scattered photon goes in a direction opposite to that of the incident photon. The electron is initially at rest. (a) How much longer is the wavelength of the scattered photon than that of the incident photon? (b) W ...continues
Eigenvalues, eigenvectors, and time evolution.
a. Given matrix A = 1 2 0 where i found the eigenvalues to be 3hw, 0, -3hw. 2 0 2 0 2 -2 then if at t=0 state-vector is 1 THEN compute the state vector at time t. 0 ...continues
