Momentum representation of the harmonic oscillator wavefunctions. (a) find the momentum representation of the ground-state wavefunction of the harmonic oscillator, ie. po. hint: proceed analogous to how we solved for (2 points) the position wavefunction in class. (b) find 〈 1) by applying the raising operator in the momentum basis l point (c) transform 〈 0) and 〈pl1〉 into the position basis and compare your results with problem #1, part (a). you may use software to carry out the integrals. 1 point (d) calculate the products arap for lo) and |1) using the representations you found in problem #1 and this one. you may use software to carry out the integrals. compare with what we found in class using the raising/lowering (1 point) operator method.

The particle in a two-dimensional well is a useful model for the motion of electrons around the indole ring (3), the conjugated cycle found in the side chain of tryptophan. we may regard indole as a rectangle with sides of length 280 pm and 450 pm, with 10 electrons in the conjugated p system. as in case study 9.1, we assume that in the ground state of the molecule each quantized level is occupied by two electrons. (a) calculate the energy of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels. 9.27 electrons around the porphine ring (4), the conjugated macrocycle that forms the structural basis of the heme group and the chlorophylls. we may treat the group as a circular ring of radius 440 pm, with 20 electrons in the conjugated system moving along the perimeter of the ring. as in exercise 9.26, assume that in the ground state of the molecule quantized each level is occupied by two electrons. (a) calculate the energy and angular momentum of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels.

Determine the maximum r-value of the polar equation r =3+3 cos 0

Select all of the following that are equal to an impulse of 20 unitsa) force= 5, time= 5.5b) force= 25, time= 0.8c) force= 0.1, time= 200d) force= 10, time= 2(its b, c, and d)(also in order to find answer they have to add to get the unit)ex= 25x.8=20 or .1x200=20