Home Particle In A Ring
Position Arrowheads correspond to units of distance.
Real Axis of Wavefunction
Imaginary Axis of Wavefunction
Momentum Display Momentum Wavefunction
Play Speed(1=RealTime):
X Scaling:
Y Scaling:
Mass: 5
Radius: 2
*No. of points:
psi equals the sum of coefficents multiplied by their corresponding n-ket
*Manually Input Coefficients:
Smart Mode
Start N
Define Cn=f(n,t,u,w)
*Min value of n: 16
*Max value of n: 16
u = 1 + 0i
w = 1 + 0i
*f(n,t,u,w)=
*Needs "Apply"

Help- "Smart Mode"

Automatically spreads out coefficients around 0.

If you type in an even number of coefficients then it skips over 0.

So if you type [4,1i,2,-1] then these will apply to states where n=-2,-1,1,2

And if you type [1,2i,-1,3,-2] then these will apply to states where n=-2,-1,0,1,2

All other states have their coefficient set to zero.

Help- "Particle In A Ring"

In this situation you have wavefunction that's confined to a circle. This simulation is the closest to what's called a "free particle" which just means something moving uninfluenced in a vacuum.

In this simulation there are both positive and negative values for "n" which correspond to the particle moving in opposite directions. In the other simulations this doesn't happen because there are endpoints to the region where the particle can be. Those endpoints mean that n=3 and n=-3 states have the same energy. We call states with different "quantum numbers", but equal energy "degenerate" states.

Something interesting in this simulation is seeing the particle move in two directions at once. If you type any number of 1s in the manual coeficients box (with smart mode on) you should see that the forward and backward states cancel out and the particle doesn't really have a definite motion in either direction.