For a particle with principle quantum n in a box of size L, what is the average value of momentum? What is the average value of momentum squared?
momentum is hn/2L where h is that constant
momentum squared is h2n2/4L2
For a particle with principle quantum n in a box of size L, what is the average value of momentum? What is the average value of momentum squared?
An electron in an atom is in the n=2 state, where n is the principle quantum number. What possible values could the orbital quantum number take? What possible values could the magnetic orbital quantum number take? What are the possible values of the Orbital Angular Momentum (L)? What are the possible values of ???
(V.4) A particle is observed to have orbital angular momentum quantum number 2. The z component of the angular momentum is measured to be Lz2h. A second particle is observed to have orbital angular momentum quantum number l2-2 and a z component ha = +2 V1(1 +1), what are the possible outcomes, and with what relative probabilities? What is the expectation value (L)'? h. If a measurement is made of the total angular momentum L-h
for a one dimensional particle in a box, write an integral expression for the average value, or expectation value, of the momentum of the n=1 state
2C. In quantum mechanics what is the maximum angular momentum of an electron in the n = 4 quantum state of the hydrogen atom? 2D. In quantum mechanics what is the maximum value for the z-component of the angular momentum of the electron in the n = 3 quantum state of the hydrogen atom?
Problem 3. Calculate a) the average momentum and b) the average position of a particle, of mass m in a one-dimensional box of length L by evaluating specific integrals.
12. Which of the following sets of quantum numbers ( n, l, m l,ms) is not allowed? a. 2 1 0 + b. 2 2 1 + c. 3 1 0 – d. 5 0 0 + e. 4 2 –1 – 14. Which of the following atoms is the most electronegative? a. Al b. B c. Cs d. N e. Na 15. The Pauli exclusion principle states that a. an electron can have either particle character or wave character. b. no two electrons in the same atom can have the...
According to the Heisenberg uncertainty principle, what is the minimum possible 1D box size (L) capable of trapping an electron (me = 9.109 × 10−31 kg)
Problem 3: Time-Independent Perturbation Theory Consider the particle in a 1D box of size L, as in Fig. 3. A perturbation of the form. V,δ ((x-2)2-a2) with a < L is applied to the unperturbed Hamiltonian of the 1D particle in a box (solutions on the equation sheet). Here V is a constant with units of energy. Remember the following propertics of the Dirac delta function m,f(x)6(x-a)dx f(a) 6(az) が(z) = = ds( dz E, or Ψ(x)-En 10 0.0 0.2...
Translational motion in ID 2. Calculate a) the average square of linear momentum, b) the average position of a particle, and c) the average square of the position of a particle of mass m in a box of length L by evaluating specific integrals (for arbitrary n).
Problem 3 Consider a particle with total angular momentum quantum number l (1) Write down the matrix L, representing L using the basis formed by {|l, m)], which are co-eigenstates of I2 and L. Choose the order of the basis vectors such that the diagonal matrix elements of L, are in descending order. [10 points] 2) Write down the matrix representations of L+ and L using the same basis for representing L. [20 points] (3) Write down the matrix representations...