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- a Construct Slater determinant wavefunctions for Be and B. Hint: Although you need only include one p orbital for B, you should recognize that up to six possible determinants can be constructed. b How many different Slater determinants can be constructed for C, assuming that the p electrons spread out among the available p orbitals and have the same spin? How many different Slater determinants are there for F?a What is the ratio of energy levels having the same quantum numbers in a box that is 1nm1nm1nm and a box that is 2nm2nm2nm? b Are the degeneracies of each set of quantum numbers the same for both cubical boxes? Explain your answer.Is the uncertainty principle consistent with our description of the wavefunctions of the 1D particle-in-a-box? Hint: Remember that position is not an eigenvalue operator for the particle-in-a-box wavefunctions.
- For an unbound or free particle having mass m in the complete absence of any potential energy that is, V=0, the acceptable one-dimensional wavefunctions are =Aei(2mE)1/2x/h+Bei(2mE)1/2x/h, where A and B are constants and E is the energy of the particle. Is this wavefunction normalizable over the interval x+? Explain the significance of your answer.Show that the normalization constants for the general form of the wavefunction =sin(nx/a) are the same and do not depend on the quantum number n.What is the degeneracy of an h subshell? An n subshell?
- What are x,y, and z for 111 of a 3-D particle-in-a-box? The operators for y and z are similar to the operator for x, except that y is substituted for x wherever it appears, and the same for z. What point in the box is described by these average values?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?Under what conditions would the operator described as multiplication by i the square root of 1 be considered a Hermitian operator?