What if a particle had infinite mass?

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.
  • #1
trelek2
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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?
 
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  • #2
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.
 
  • #3
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!
 

FAQ: What if a particle had infinite mass?

What does it mean for a particle to have infinite mass?

When we say a particle has infinite mass, it means that it has an immeasurably large amount of mass. In other words, it would have an infinite amount of inertia, making it impossible for anything to accelerate it or change its direction.

Is it possible for a particle to have infinite mass?

No, it is not possible for a particle to have infinite mass in our current understanding of physics. The concept of infinite mass violates the principles of relativity and would result in many paradoxes and inconsistencies.

What would happen if a particle had infinite mass?

If a particle had infinite mass, it would have an infinite amount of energy, according to Einstein's famous equation E=mc^2. This would have a range of consequences, such as warping space-time and causing gravitational singularities.

Can a black hole be considered a particle with infinite mass?

No, a black hole is not considered to be a particle. It is an object with a singularity at its center, where the laws of physics as we know them break down. While it has an incredibly large mass, it is not considered to have infinite mass.

How does the concept of infinite mass relate to the idea of the Higgs boson?

The Higgs boson is a particle that is responsible for giving other particles their mass. However, it does not have infinite mass itself. In fact, one of the main reasons for the existence of the Higgs boson is to explain why particles do not have infinite mass.

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