Question

3. (40 pts) A harronic oscillator has normalized energy eigenstates l e,) , n-0, 1, 2, The ladder operators have the properties and The momentum operator is given by |m/s 0)- (%)+2in)-in Suppose the oscillator is initially in the state a) (5 pts) What is the state |W() at later tiriest0 b) (5 pts) Write!ψ(1) as a column vector in the basis {1%), 1%), 19)} (5 pts) Write ()as a row vector in the basi),19) d) (5 pts) Construct the matrix for a, in the basis { |Po), la) , 1%) } e) (5 pts) what is the matrix or a in the basis { | Po), 1%) , 19) } f) (5 pts) what is the ratrix for p in the basis {|Po>,19),1%)} g) (10 pts) Find the position expectation value(p(1)for the state y (1).

Answer 1