Finite Square Well

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

Wave packet problem

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.

Potential Barrier

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.

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 state of lowest energy; explain briefly the form taken by in the direction of region x. c) A particle of mass m with energy Etot greater than W1 but less than W2 is projected from the right; give a short classical account of its subsequent motion, including expressions for speed.