Quantum Mechanics Answers

Calculate the mean kinetic and potential energies of a simple harmonic oscillator
which is in its ground state.

) The wavefunction for a particle is defined by:
ψ (x)={ N cos(2πx/L) for - L/4 ≤x≤ L/4
0 otherwise


Determine
i) the normalization constant N, and
ii) the probability that the particle will be found between x = 0 and x = L / 8. (5+5)

For the operator A = a x + i b p where a and b are constants, calculate [A, x] and
[A, A].

Use Heisenberg’s uncertainty principle to estimate the ground state energy of the
harmonic oscillator.

A body of mass 6kg is at rest when a force of magnitude 30 N on the body. After 10s what will be kinetic energy?

The wavefront for a particle is defined by:
Ψ(x)= {Ncos(2πx/L) for -L/4≤x≤L/4
{0 otherwise
How to determine:
i) the normalisation constant N,
ii) the probability that the particle will be found between x=0 and x=L/8.

Is it possible with a quantum computer and an infinite energy source to separate time from space. What my theory is is that if an object occupies not only space but also time in that space. If you were able to swap that occupied space/time with unoccupied space/time, could it be done and how?

Let A and B be vector operators. This means that they have certain
nontrivial commutation relations with the angular momentum opera￾tors. Use those relations to prove that A·B commutes with Jx, Jy, and
Jz.

Find the probability distributions of the orbital angular momentum
variables L2 and Lz for the following orbital state functions:
(a) Ψ(x) = f(r) sin θ cos φ,
(b) Ψ(x) = f(r)(cos θ)2,
(c) Ψ(x) = f(r) sin θ cos θ sin φ.
Here r, θ, φ are the usual spherical coordinates, and f(r) is an arbitrary
radial function (not necessarily the same in each case) into which the
normalization constant has been absorbed

Answer in 3 to 4 sentences

1. why can't we see matter as a particle and a wave?
2. use a similar example to explain the wave particle duality?