Matrix representation of an operator.

Find the eigenvalues and eigenvectors of the operator. Normalize the eigenvectors. See attached file for full problem description.

Commutators and the harmonic oscillator

Commutators and the harmonic oscillator. See attached file for full problem description.

Operators and Eigenstates

If |0> and |1> denote the two eigenstates of N corresponding to the eigenvalues 0 and 1, respectively, show that c† |0> = |1> and c |0> = 0

Matrix representation

Find the unitary transformation which transforms into a diagonal matrix and verify that the diagonal elements are 0 , 3, and 3

A 1000 newton crate is being pushed across a level floor at a constant speed by a force of 300 newton at an angle of 20 degrees

A 1000 newton crate is being pushed across a level floor at a constant speed by a force of 300 newtons at an angle of 20 degrees below the horizontal A-what is the coeffecient of kinetic friction between the crate and the floor. B-if the 300 newton force is instead of pulling the block at an angle of 20 degrees above the horizontal -What will be the acceleration of the crate assume that the coeffient of friction is the same as found in A.