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...
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
Schrodinger 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...
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...