Angular Momentum

A system with is measured to have . (a)What is the probabilty of measuring ? (b) In the state , find , , and . (see attachment for question with figures)

Semi-infinite potential: Derivation of the transcendental equation for the case of E < Vo and finding the reflection coefficient for the case of E > Vo

A semi-infinite potential well is given as shown in the figure. ---------- Figure ------------------- (a) Consider the case when (0 Vo is incident from the right into the potential region. Calculate the coefficient of reflection for the particle. Please see the attached file for figure and equation.

Commutation relations and the uncertainty principle

Consider two hermitian operators A and B which satisfy the following commutation relation: [A, B] = AB-BA=iC, where C is also a hermitian operator in general. Let us introduce a new operator Q defined by: Q=A+ iλB, with λ being a real number, and consider the following scalar product: Where is any normalized wave function? (a)Show that Eq. (1) leads to the following result: (b)Define the uncertainties as follows: With U≡A - and V≡B - < B>, respectively. Show that [U, V] = [A, B] = iC (c)Thus, replacing A, B in (a) by U,V, we obtain: Regarding I(λ) as a quadratic function ofλ, show that I(λ) is minimum when (d)Let A=X, B= px, show that t... click for more

De Broglie Hypothesis

De Broglie Hypothesis. See attached file for full problem description.

Mean position in a 1-D harmonic oscillator

Obtain the mean position, , for a particle moving in a 1-D harmonic oscillator potential, when the particle is in the state with normalized wavefunction: Y(x)= ((a/(4*pi))^.25)*(2ax^2-1)*exp((-ax^2)/2)