# Does the Schrodinger equation describe particles popping in and out of existence?

Sparky_
Hello -
A few questions I have after watching Brian Green’s The Elegant Universe –
Within the video Dr. Green shows a neat way to view the different scales relativity and quantum mechanics are involved with. He takes an elevator to a top floor to show relativity’s applicable scale. He steps out of the elevator to show planets below him. The fabric of space-time is show as a graph paper grid – everything was very calm.

He takes the elevator down (way down) and steps out to show the quantum scale. The environment was very noisy (I compare it to watching an oscilloscope with the voltage scale set way down – lots of jitter and noise.

Within this jitter it was explained that particles and their corresponding anti-particles were briefly popping into and out of existence.

From my very limited experience with the Schrodinger equation – I see that the limits on the integral can be used to set a time range and / or volume range and the solution is a probability of that event happening within that range.

Does Schrodinger equation describe these particles / anti-particles popping in and out of existence?
If one was to solve a problem for a particular particle – an electron popping into existence – is there a parameter within the Schrodinger equation that is particle specific? Meaning how would equation differ by solving the probability of an electron popping into existence versus a different particle popping into existence?

Thanks
Sparky_

## Answers and Replies

Mentor
In nonrelativistic quantum mechanics, there are no particles appearing/vanishing. You need quantum field theory, there you have operators which can produce and annihilate particles in the hamiltonian. If you use that in the Schrödinger equation, it can handle creation and annihilation of particles.

Meaning how would equation differ by solving the probability of an electron popping into existence versus a different particle popping into existence?
An electron cannot simply be created, you need an additional positron popping up. And if those do not interact with other particles in the right way, they have to vanish again. However, you can calculate the probability for all allowed processes - at least in theory.

Nii Sapu
There is a very simple answer: No.

klawlor419
As far as I know all the Schrodinger equation tells you is, if you have a particle or system of particles how the wavefunction of that particle or system behaves spatially and temporally.