Exercise 2 Consider a random variable X with E]5 and VarX 16 (a) Calculate P(lz-5 < 6) if X follows a normal distribution. (b) Use Chebyshev's inequality to provide a lower bound for P(-5). (No longer assume X is normal.)
Given a 3-dimensional particle-in-a-box system with infinite barriers and Lx=5nm, Ly=5nm and Lz=6nm. Calculate the energies of the ground state and first excited state. List all combinations of values for the quantum numbers nx, ny and nz that are associated with these states.
2, Explicitly construct the three 3 × 3 matrices that represent (a) Lx, Ly, and Lz in the space of 1 1 functions: (Li/m , m' s(1-1, ml Lill = 1,m') 1m where i = x, y, z. (b) Show by explicit calculation that these three matrices obey the commutation relations of angular momentum (c) Find the matrices that represent L.+, L, and L2
Show that the function defined by (2)= is analytic on the open unit disk {lz| < 1} and that |(rA) Remark: This function does not extend analytically to any larger open set than the unit disk +o0 as r-1 whenever A is a root of unity
Show that the function defined by (2)= is analytic on the open unit disk {lz|
Sketch the vector model for l = 3 and for every vector, show the Lz value.
heres the previous problem. need number 3 done.
3. (5 pts) Ulse the method of undetermined coeffcients to find the solution to the system in problem 2 with initial condition given by y1(0)-0, y2(0)- yi(0) -0, v2(0) 0 2. (10 pts) Use the method of variation of parameters to find the general solution of the systam y' - Ay+g(0) where A is the matrix 1 2, and g(t) 0 A-2 1
3. (5 pts) Ulse the method of undetermined coeffcients...
2. Integrate by parts S x2 e e-* dx . 3. Use the method of partial fractions to evaluate S ( 5x-5 3x2-8x-3
Please help me to answer the question number 2,3 and
4
Thank you
t. Determine Vab e) 2. . Determlne P,e power tage and detming Pr 3 Drau We phao urmfV and Congpret ench Compneanf u. Delamning the total inedance (ota) asor sa .nmn an omn. İsa 2 Fy Lz C
t. Determine Vab e) 2. . Determlne P,e power tage and detming Pr 3 Drau We phao urmfV and Congpret ench Compneanf u. Delamning the total inedance (ota) asor...
Given the system of linear equations 5?1 + 2?2 + ?3 = 45 −2?1 + ?2 − 3?3 = −4 4?1 − ?2 + 8?3 = 2 a. Write the augmented matrix b. Solve the system by Gaussian elimination & backward substitution method.
Two noninteractingidantical spin-/2 fermions mass m are confined to a cubical box with the potential V(x, y,e) oo otherwise ppose the sstem f two particlesits g rownd state. Findthe wave function the total o fa and the s4uari f the total spin. rg Eo ener sP (b) What is the energy El and degenerac," of the first excited state ? Find v linear! independent wave functions with enerJyEl for the two fermions
Two noninteractingidantical spin-/2 fermions mass m are confined...