6. Show that for an infinite square well (p2-CanE), and compute (p2〉 for the ground state.
A particle is in the ground state of a symmetric infinite square well with Vx) O for -a/2<x<+a/2, and infinite elsewhere. (a) The well then undergoes an instantaneous symmetric expansion to -a <<< ta. Calculate the probabilities of the particle being found in each of the three lowest energy states of the larger well. (b) Instead, suppose that the well expansion takes place adiabatically. Again, calculate the probabilities of the particle being found in each of the three lowest energy...
5) A particle of mass m is in the ground state of the infinite square well 0 < x < a At t-0 the right hand wall suddenly moves to x = 2a, doubling the size of the well. Assume that this expansion happens on a time scale so fast that the initial wave function (at t0+) is the same as just before the expansion (at t-0-) (This is called the "sudden" approximation.) a) What is the probability that a...
2. Find the expectation value for <p2 > for the ground-state wave function of the infinite 1-d square well. Here p = -i(hbar) d/dx is the (linear) momentum operator
In an infinite square well , probabilities for the ground state, n=1,. Consider now the n=3 state ((x)n=3 is shown in fig. 6-4). Between 3L/8 and 5L/8, what is the probability of finding the electron?
An infinite square well and a finite square well in 1D with equal width. The potential energies of these wells are Infinite square well: V(x)=0, from 0 < x < a, also V(x) = , elsewhere Finite square well: V(x)= 0, from 0 < x < a, also V(x) = , elsewhere The ground state of both systems have identical particles. Without solving the energies of ground states, determine which particle has the higher energy and explain why?
6. (a) Consider the infinite square well again. Let the width of the well be a and the particle mass be m. Find an expression for the probability that a particle in the state, vi will be found in the region a/4 <x<3a/4. (b) Repeat part (a) for the nth eigenstate, yn, for arbitrary n. Show that the answer reduces to the classical value of 2 as n 00.
A proton is in an infinite square well of dimension L = 2fm (i.e. 2 ×10-15m). a) What is the ground state energy? Show all work. b) What would be the energy of a photon emitted if the proton in the well went from the n=2 state to the n=1 state? Show all work.
Exercise 5 Consider a particle in an infinite square well of length a. The particle is initially in the ground-state. The width of the potential well is suddenly changed by moving the right wall of the well from a to 2a. What is the probability of observing the particle in the ground-state of the new expanded well ?
A particle in an infinite well of width L is in its ground state. a) If L is 30 cm, what is the ground state energy? (3 marks) Where is the particle most likely to be found? Use sketching to further explain. (4 marks)
The force that binds protons and neutrons in the nucleus of an atom is often approximated by an infinite square well potential. A proton is confined in an infinite square well of width 1 x 10^-14 m. Calculate the energy and wavelength of the photon emitted when the proton undergoes a transition from the first excited state (n = 2) to the ground state (n = 1). In what region of the electromagnetic spectrum does this wavelength belong? Show all...