We can use a quartic function function to represent this potential as shown below. Using the first order perturbation theory for particle in a box, calculate the ground- state energy: V(x) = ca 0
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- please solve it as soon as possibleA particle is constrained to move in an infinitely deep square potential well, spanning from 0 < x < a. Suppose we add a delta function bump in the center of the well to produce the perturbation: H0 = (x−a=2) (1) Where is a constant. Find the first order correction to the nth allowed value of the energy. Explain why there is no correction for even n.Calculate the expectation value of the momentum (p) and the square of the momentum (p2) for the particle in a box of length L and infinite potential outside the box.
- Derive the Nernst Equation from the definition of the free energy, G.Consider a particle of mass m moving in the following potential V(x)= v1 for xv2. What is the grown state energy? And the normalized ground sate funcionConsider a finite potential step with V = V0 in the region x < 0, and V = 0 in the region x > 0 (image). For particles with energy E > V0, and coming into the system from the left, what would be the wavefunction used to describe the “transmitted” particles and the wavefunction used to describe the “reflected” particles?
- Find out the values of potential at local minima and/or maxima point(s).Plot the first three wavefunctions and the first three energies for the particle in a box of length L and infinite potential outside the box. Do these for n = 1, n = 2, and n = 3The essence of the statement of the uniqueness theorem is that if we know the conditions the limit that needs to be met by the potential of the system, then we find the solution of the system , then that solution is the only solution that exists and is not other solutions may be found. If we know potential solutions of a system, can we determine the type of system that generate this potential? If so, prove the statement! If no, give an example of a case that breaks the statement!
- I need the answer as soon as possibleA particle of mass m is confined within a finite square well of depth V0 and width L.Sketch this potential, together with the form of the wavefunction and probability density for a particle in the lowest energy state. Briefly outline the procedure you would follow to determine the total number of energy eigenstates that can exist within a given finite square well.what are the possible results that may be obtained upon measuring the property lz on a particle in a particular state, if its wavefunction is known to be Ψ, which is an eigenfunction of l2 such that l2Ψ=12ℏΨ? SHOW FULL AND COMPLETE PROCEDURE IN A CLEAR AND ORDERED WAY