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7) Calculate the average of the operator of angular momentum <i >z<ylî ly> for: (a) lỤ=1,1>...
orbital angular momentum For an orbital angular momentum, measurement of L and Lz produces ħ²1 (1+ 1) and mħ respectively. What are the values of < Lx > and AL,? Assume 1 = 1, m probability for Lx = -ħ? 1, what is the
Given z = 2 y2 – 3xy , find the slope of the surface at (1,1,-1) in the direction of ū =< 2,3>
(2.) Consider the orbital angular momentum operator defined in terms of the position and momentum operators as p. Define the angular momentum raising and lowering operators as L± = LztiLy. Use the commutation relations for the position and m omentum operators and find the commutators for: (a.) Lx, Lz and Ly, Lz; (b.) L2, Lz; (c.) L+,L
• Problem 7. For a wave-function W.(x) = (2/a)" sin(x/a) calculate the average position (<x>). Is the function W.(x) = (2/a) sin(x/a) an eigenfunction of the x operator?
4. Let Z ~ N(0,1) be a standard normal variable. Calculate the probability (a) P(1 <Z < 2). (b) P(-0.25 < < < 0.8). (c) P(Z = 0). (d) P(Z > -1).
Particle in a box. (a) Let H=L?([0,L]) (square integrable wave functions on the interval 0 < x <L). Show that the wave functions Yn(x) = eilanx/L, n=0,1,-1,2, -2,... (6) form an orthonormal system in H. Is this system a basis? (b) Show that the wave functions Yn are eigenstates of the momentum operator p on H= L?([0,L]). Hence, show that the variance Ap in the state Yin vanishes. What is the variance Ať in the state Yn? Why is the...
A) B) C) 1 Find the Laurent series for 22 +22 for 0 < 121 < 2 Find the Laurent series for (z+2)}(3-2) for 2 – 3) > 5 1 Find the Laurent series for z2(z-i) for 1 < 12 – 11 < V2
Solve: Laurent series h(z) - Z O CIZ + 11 <3 (2+1)(2-2)
Exercises 4.2 ove that the sequence (1 + z/n)"; n = 1, 2, 3,..., converges uni- ly in Iz <R < , for every R. What is the limit? 1, afdos se converge? diverge?
Problem 3. At some moment of time, an electron in the hydrogen atom is prepared in the state y=1/12(R21Y1-11T>+ R32Y2011>). Determine the expectation values of (a) Î, Îz - the square of the orbital angular momentum and its projection on the z-axis, (b) Ŝ2, S2 - the square of the spin and its projection on the z-axis, (c) ſ2 = (Î + Ŝ2 - the square of the total angular momentum. Do not use calculus, use algebra in this problem.