Wavefunctions of a finite square well. See attachments for details.
Please refer to the attachment for the problem. For the plot, please use Mathematica if possible. Also , the last part ask to evaluate the integeral numerically, which requires using mathematica.
See attached file for full problem description.
The question deals with matrix representation of the ladder operators of the quantum harmonic oscillator, the orthonormality of the eigenfunctions and eigenfunction expansion series of the wave functions to show that the solutions can be Hermite polynomials. Please help ASAP even with only parts A and B.
Bound particle in a finite square well/potential well
Question 1 Figure 1 represents a particle of total energy Etot bound in a finite potential well, with potential energy function Etot (x). (see attachment for figure and question) a)From figure 1 express Epot(x) as a function of x. b)For the range of x covered by figure 1 sketch the wave function , of the bound sta ...continues
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 no ...continues
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 ...continues
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 ...continues
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 t ...continues
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} ...continues
