# What if a particle had infinite mass?

• trelek2
In summary, when taking the mass of a particle to infinity, the wave function will become narrow and the particle will fall under classical mechanics. In the case of an infinite potential well, the wave function can be sketched by taking the solution for a particle-in-a-box and letting the mass approach infinity. This results in a particle that does not oscillate and has zero energy, leading to unphysical outcomes.

#### trelek2

Hi, I'm wondering what will happen to the wave function of a particle when we take its mass to infinity.

Suppose the infinite particle is in an infinite potential well, how do we sketch the wave function?

trelek2 said:
Hi, I'm wondering what will happen to the wave function of a particle when we take its mass to infinity.

Suppose the infinite particle is in an infinite potential well, how do we sketch the wave function?
I didn't run any number. I don't think an infinite mass is realistic. The best I can think of is to let the mass tends to infinity. When the mass is "big", you should fall over classical mechanics. That would mean that in the "infinite potential" the wavefunction is probably narrow (which means a somehow well defined position).
Just a guess though.

This is unphysical, but...

Simply take the solution to the particle-in-a-box and let m->inf. http://en.wikipedia.org/wiki/Particle_in_a_box

The w in the e^-iwt term goes to zero, so the whole thing vanishes. You're left with a particle that doesn't oscillate at its initial state, which is going to be some superposition of Acos(kx) + Bsin(kx).

Looking at the energy equations, you can see this quickly leads to nonsense; for example, no matter the energy level of the system (n) the system would have zero energy!