Home Particle In A Box
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: 25
Length "L": 4
*No. of points:
psi equals the sum of coefficents multiplied by their corresponding n-ket
Represent as Reflection:
*Manually Input Coefficients:
Define Cn=f(n,t,u,w)
*Max value of n: 16
u = 1 + 0i
w = 1 + 0i
*f(n,t,u,w)=
*Needs "Apply"

Help- "Particle In A Box"

This is a particle perfectly confined to a region of Length "L". Or, if you like, the quantum equivalent of a guitar string.

In reality this situation is very unphysical. In order to perfectly confine the particle to a region, you need an infinite wall of energy to stop it leaking out.

But assuming it to be possible, greatly simplifies a lot of the maths, in fact each energy state is just a sine or cosine wave of a specific frequency. This is because, like a guitar string, each of the end points are fixed in place at 0, meaning only certain frequencies are allowed. In a guitar string the waves bounce of the end points and interact with the waves coming in the other direction. A very similar phenomenon happens in this simulation and you can see the particle "interacting with itself" by checking the box marked "Represent As Reflection".

See Also: Standing Waves, Self-Interaction

Help- "Reflection"

This will display show a decomposition of the wavefunction as two "free particles" moving in opposite directions. By adding these two together you get the original wavefunction.

At each wall the arrows pointing into it will be exactly opposite the arrows coming out of it. This may not seem like a reflection but when polarised light reflects off a surface it rotates by a full 180 degrees in the same way and so does the sound wave in a guitar string. This exact opposition also means they cancel out and keep the waveunction at zero at each of the end points.

See Also: Standing Waves, Sine and Cosine as Exponentials