Calculate the normalization factor of a wavefunction

A quantum system has a measurable property represented by the observable S with possible eigenvalues nħ, where n = -2, -1, 0, 1, 2. the corresponding eigenstates have normalized wavefunctions Ψn. the system is prepared in the normalized superposition state given by, *Please see attached for equation* Where N is a normalizing factor. i) Calculate N. ii) Write down the probabilities of the following measurements of *see attachment for numbers*

entangled states of wavefunctions.

Suppose that a pair of electrons, A and B, were described by the following wave function: (see attached for equations) (I have rewritten this equation as I believe some of you are having problems reading the text.) What property specific to entanglement must the wavefunction describing an entangled state of two particles A and B possess? Using this criterion, determine whether or not the wavefunction above describes an entangled state. See attachment for full question and details

particle in a one dimensional box

. Consider a particle of mass m which can move freely along the x-axis anywhere from x+-a/2 to x= a/2, but which is strictly prohibited from being found outside this region. The particle bounces back and forth between the wall at x=a/2 of box. The walls are assumed to be completely impenetrable, no matter how energetic is the particle. Using the following wave function and time dependent Schroedinger equation: y(x,t)= Acos (px/a)e^-I(E/h)t, for -a/2,x,a/2 0 for x£-a/2 or x³a/2 Determine the lowest energy state E for the system Determine the expectation values of x, p, x², and p². Explain where these values come ... click for more

Scattering Problem

Demonstrate, for a particle scattering from a finite-range, spherically symmetric potential V(r), which is weak enough so that the Born approximation for symmetric potentials is valid, that the total cross section, at very low energies, is a linear function of the energy σ(E) = σ0(1+αE), where σ0 is related to the volume integral of the potential... Please see attached for full question.

Harmonic Oscillator

Consider the 1-D harmonic oscillator, with Hamiltonian H=p²/2m+½mw²x²=hw(a†a+1/2), and with energy eigenstates H|n}=En|n}=hw(n+1/2)|n}. The eigenvectors of the annihilation operator a are known as coherent states: a|z}=z|z}, where z is in general a complex number (a is not Hermitian, so z is not necessarily real). Take |z} to be normalized: {z|z}=1. a) Find and expression for |z} as a linear combination of the eneergy eigenstates |n}. Make sure it is normalized. Calculate {z1|z2}. Please see attached for full question. Also { and } are not the correct symbols, please see attached for proper format.