Recent content by Nicolaus

Qualitatively, though, the initial state is a non-localized particle with well-defined energy, traveling to the right. Would this mean that the second integral (with the reflection coefficient) would be zero since that represents a particle moving in the left direction (reflected part), which...

I am getting Dirac-Delta Functions for φ(k). Does this sound right?

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Correct. If I want a Re-Im representation, how would I go about plotting that on Matlab? Actually, it would be good to know how to plot both types. Thanks

I should have specified; my intent was not for that to represent an infinite series, but rather other arbitrary terms for a linear combination of a finite number of energy eigenfunctions of the infinite square well.

Hi, I am wondering how to plot a complex function of the form: Ψ(t) = Ansin(n⋅pi⋅x/L)e-iEnt/h + Bnsin(m⋅pi⋅x/L)e-iEmt/h + ... + where m and n are known eigenvalues of the infinite square well with corresponding energy En, for any particular x? So, this will be a function of solely t. Any help...

Homework Statement Say there exists a delta potential V(x) = α(x-L). Solve the eigenvalue problem to yield the energy eigenstates. Say a quanton is in an initial state given by Ψ(x)=Aeikox at t=0. What is Ψ(x,t)? Homework Equations Schrödinger Eqn. The Attempt at a Solution I solved the first...

I made a mistake, the equation in-between a and b should read: V(r) = kr^4/20 - c1/r +c2 The boundary conditions should be Vinside(a) = Vbetween(a) and Vbetween(b) = Vout(B) for continuity; am I missing any other conditions? I know there's the discontinuous derivative of potential = some...

Homework Statement ut +ux = 0 subject to u(t,x) = x on x^2 + y^2 = 1 Is this a well-posed PDE BVP? Homework EquationsThe Attempt at a Solution This is an easy one to solve: u(t,x) = f(x-t) I let t(0) = 0 as an initial condition, and so t=s => x= ts + xo, where x(0) = xo s is the variable...

Homework Statement Two grounded spherical conducting shells of radii a and b (a < b) are arranged concentrically. The space between the shells carries a charge density ρ(r) = kr^2. What are the equations for the potential in each region of space?Homework Equations Poisson's and LaPlace's in...

Homework Statement Say, for example, a wave function is defined as 1/sqrt(2)[ψ(1)+ψ(2)] where ψ are the normalized stationary state energy eigenfunctions of the ISQ. Now, say I make a measurement of position. What becomes of the wavefunction at a time t>0 after the position measurement (i.e...

So Region A looks like a triangle with its top vertex at the origin (the entire triangle is below the horizontal x-axis and its y coordinates range from -1 to 0); this region is bounded by x=y to the left and x=-y to the right. I am asking what values of a are allowed such that the union of...

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I've tried this, and it appears to work. Maybe I'm missing something. What's your reasoning for this?

Homework Statement Find all values of a such that this set is a type II region (i.e. the bounds of x can be represented as functions of y, while the bounds of y are constant valued) -1<y<0, Y<x<-y (union) 0<y<1, -y+a<x<y+a Homework EquationsThe Attempt at a Solution I arrived at a being any...