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# Wavefunction

### 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

### Normalization of a wavefunction: Example problem

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 normalizin

### {21.24} A 3kg particle has a velocity of (3i-4j) m/s. Find the magnitude of its momentum?

A 3kg particle has a velocity of (3i-4j) m/s. Find the magnitude of its momentum? ============================================= Answers: a) 9kg m/s b) -12 kg m/s c) 15 kg m/s d) 3 kg m/s ################################################## A sinusoidal wave is described by y=(0.30m)sin(0.20x-40t). Determine the wave speed.

### Potential Barrier Question

Consider the potential barrier v(x) = + Vo, |x| < a 0, |x| > a Solve for the transmission T and the absolute square |T|^2 for both cases E < Vo & E > Vo. Express the answer as |T|^2(x), where x = (2mEa^2)/h^2 = 1. Plot |T|^2(x) for both E <Vo & E > V. *Note: Please plot both cases on the same graph. (

### Wavefunctions calculations in a finite square well.

Wavefunctions of a finite square well. See attachments for details.

### Schrodinger Equation for a Harmonic Oscillator

The schroedinger equation for harmonic oscillator can be written: E*psi = [(h^2)/2m][((d^2)*psi)/(dx^2)] + (1/2)kx^(2*psi) Write and formally differentiate each term to get the second derivative with respect to X. Put it all into the equation as shown and you will see that there will be an infinite number of possible solu

### Fermions in harmonic potential.

Two identical, non-interacting spin-1/2 fermions are placed in the 1-D harmonic potential V(x) = (1/2)m ω2x2, Where m is the mass of the fermion and ω is its angular frequency. a. Find the energies of the ground and first excited states of this two-fermion system. Express the eigenstates corresponding to these two

### The Intercepts for Time and Location on a Sine Curve

See attached file. A traveling wave on a wire is expressed by the equation: (1) y= .24 sin (11x - 16t). Distances are in meters, times in seconds. PART a. On a general sine curve that you see in ATTACHMENT #1, Show a properly located y axis for the graph of y(x) at t= .25 sec. Calculate and label the y intercept and thr