Question

In: Physics

Calculate the wavefunction and energy levels for the infinite square well. Go through the full calculation,...

Calculate the wavefunction and energy levels for the infinite square well.
Go through the full calculation, using boundary conditions and normalization. Then,
calculate < x > and < p > for the system.

Solutions

Expert Solution

I will be glad to see your comment if you have any query and thumb up if you are satisfied. Thanks...


Related Solutions

An electron is in the ground state of an infinite square well. The energy of the...
An electron is in the ground state of an infinite square well. The energy of the ground state is E1 = 1.35 eV. (a) What wavelength of electromagnetic radiation would be needed to excite the electron to the n = 4 state? nm (b) What is the width of the square well? nm
A particle in an infinite one-dimensional square well is in the ground state with an energy...
A particle in an infinite one-dimensional square well is in the ground state with an energy of 2.23 eV. a) If the particle is an electron, what is the size of the box? b) How much energy must be added to the particle to reach the 3rd excited state (n = 4)? c) If the particle is a proton, what is the size of the box? d) For a proton, how does your answer b) change?
Find the energy spectrum of a particle in the infinite square well, with potential U(x) →...
Find the energy spectrum of a particle in the infinite square well, with potential U(x) → ∞ for |x| > L and U(x) = αδ(x) for |x| < L. Demonstrate that in the limit α ≫ hbar^2/mL, the low energy part of the spectrum consists of a set of closely-positioned pairs of energy levels for α > 0. What is the structure of energy spectrum for α < 0?
A particle in a 3-dimensional infinite square-well potential has ground-state energy 4.3 eV. Calculate the energies...
A particle in a 3-dimensional infinite square-well potential has ground-state energy 4.3 eV. Calculate the energies of the next two levels. Also indicate the degeneracy of the levels.
Calculate all of the energy levels for an electron in the finite potential well of width...
Calculate all of the energy levels for an electron in the finite potential well of width a) L = 10 Å, b) L = 50 Å, c) L = 100 Å and L = 1000 Å using the actual mass of an electron for the conduction band of the AlGaAs/GaAs/AlGaAs quantum well. Repeat problem using a) the effective mass of an electron in GaAs (electron effective mass meff = 0.067*mass of an electron)
Consider a particle in an infinite square well, but instead of having the well from 0...
Consider a particle in an infinite square well, but instead of having the well from 0 to L as we have done in the past, it is now centered at 0 and the walls are at x = −L/2 and x = L/2. (a) Draw the first four energy eigenstates of this well. (b) Write the eigenfunctions for each of these eigenstates. (c) What are the energy eigenvalues for this system? (d) Can you find a general expression for the...
Consider a particle of mass ? in an infinite square well of width ?. Its wave...
Consider a particle of mass ? in an infinite square well of width ?. Its wave function at time t = 0 is a superposition of the third and fourth energy eigenstates as follows: ? (?, 0) = ? 3i?­3(?)+ ?­4(?) (Find A by normalizing ?(?, 0).) (Find ?(?, ?).) Find energy expectation value, <E> at time ? = 0. You should not need to evaluate any integrals. Is <E> time dependent? Use qualitative reasoning to justify. If you measure...
Work out the problem of the infinite square well in two dimensions. In this case, the...
Work out the problem of the infinite square well in two dimensions. In this case, the potential is zero inside a square of sides of length L, and infinite outside the square. Find the eigenfunctions and energy eigenvalues.
A particle in the infinite square well (width a) starts out being equally likely to be...
A particle in the infinite square well (width a) starts out being equally likely to be found in the first and last third of the well and zero in the middle third. What is the initial (t=0) wave function? Find A and graph the initial wave function. What is the expectation value of x? Show your calculation for the expectation value of x, but then say why you could have just written down the answer. Will you ever find the...
Consider two non-interacting particles in an infinite square well. One is in a state ψm, the...
Consider two non-interacting particles in an infinite square well. One is in a state ψm, the other in a state ψn with n≠m. Let’s assume that ψm and ψn are the ground state and 1st excited state respectively and that the two particles are identical fermions. The well is of width 1Å. What is the probability of finding a particle in the 1st excited state in a region of width 0.01Å? Does this change if the particles are distinguishable?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT