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- a Q₁ Given = AX (a-x), A, a are = limit ofxña at tro ~ (x, 0) Constant 1- Find A for normalized (NX, o) 2- If (AV₁0) represents the wave function of aparticle find all bil in infinite square well outside the well N(x,0) find (x, t)4. Use the following diagrams to answer (a) and (b). l/2 tum (C,) a2 O Screenshot(Alt + A) H H' H, H H H. 12 um rotation А в (a) Write down the characters of the matrices representing the C2 rotation, using the basis shown in A, B, and C. (b) Write down the matrix equations and find the characters of the matrices representing the operation of reflection in the plane of the molecule, using the basis shown in A, B, and C.The particle on a ring can be used as a model for the motion of electrons around the [18]-annulene ring. See a 2-D representation of the [18]-annulene molecule below; the dashed line around the periphery of the molecule indicates the electron path. H H H H H H H H H H H H H H H We may treat the structure as a circular ring of radius 840 pm, with 18 electrons in the conjugated system moving along the perimeter of the ring. Assuming that, in the ground state of the molecule, each state is occupied by two electrons, (a) calculate the energy and angular momentum of an electron in the highest occupied level, and (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels.
- E7B.3(b) Which of the following functions can be normalized (in all cases the range for x is from x = -∞ to ∞, and a is a positive constant): (i) sin(ax); (ii) cos(ax) ex²? Which of these functions are acceptable as wavefunctions?Which of the following transitions are electric-dipole allowed?(i) 1Σg+ ↔ 1Σu+, (ii) 3Σg+ ↔ 3Σu+, (iii) π* ↔ n.What are differences between n→π* and π →π* bonding electron transition in Fluorescence? Please answer shorty at your own words. Answer should be to the point.
- (a) The trace of an n x n matrix A is defined as tr[A] = E;=1 Ai that is, summing over all the diagonal elements of Ä. Prove: tr[ÂB] = tr[BÂ] (b) Based on this, prove the “cyclic" relation of the trace. That is tr[ÂÊĈD] = tr[DÂBĈ| = tr[ĈDÂB]Which of the following functions can be normalized (in all cases the range for x is from x= (-infinity) to (infinity), and a is a positive constant): (i) sin(ax); (ii) cos(ax)e-x^2? Which of these functions are acceptable as wavefunctions? Source: Atkins Physical Chemistry 11th Edition, E7B.4(b)4-14. Determine whether or not the following pairs of operators commute. Â B (a) (b) d dx X (c) SQR (d) x². dx d² dx² d dx SQRT d² dx² d dx +2.