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- Under what conditions would the operator described as multiplication by i the square root of 1 be considered a Hermitian operator?For a particle in a state having the wavefunction =2asinxa in the range x=0toa, what is the probability that the particle exists in the following intervals? a x=0to0.02ab x=0.24ato0.26a c x=0.49ato0.51ad x=0.74ato0.76a e x=0.98ato1.00a Plot the probabilities versus x. What does your plot illustrate about the probability?What is the degeneracy of an h subshell? An n subshell?
- For a system rotating in three dimensions. what is the degeneracy of the level with I=4? What are the valid values of m,?Confirm that a Morse oscillator has a finite number of bound states, the states with V < hc ᷉ De. Determine the value of vmax for the highest bound state.Confirm that the wavefunctions of the 2D rigid rotor for m=1 and m=2 are orthogonal.
- Calculate the zero point energy of a harmonic oscillator consisting of a particle of mass 2.33 x10-2 kg and force constant 155Nm-1What is the degeneracy of a molecule rotating with J = 4?Calculate the expectation values of px and px2 for a particle in the state with n = 2 in a one-dimensional square-well potential.
- Calculate the energies of the first four rotational levels of 1H127I free to rotate in three dimensions; use for its moment of inertia I = μR2, with μ = mHmI/(mH + mI) and R = 160 pm. Use integer relative atomic masses for this estimate.If the non-normalized wave function (1-x/b)is e-x/2b, remove the normalized state.Construct the potential energy operator of a particle with potential energy V(x)=1/2kfx2, where kf is a constant