Hello everybody,(adsbygoogle = window.adsbygoogle || []).push({});

I am currently struggling with a problem that I came across while spending some free time on non-relativistic quantum mechanic problems.

Suppose we have an electron that is describe at time [itex] t_0 = 0 [/itex] by a wave function in position space [itex]\psi(x,y,z)[/itex]. Furthermore, assume that we have a Hamiltonian

[itex] \hat{H}_1 = \frac{1}{2m}\left [ \mathbf{p}+\frac{e}{c} \mathbf{A}_1(\mathbf{r}) \right ]^2[/itex]

with charge e, mass m and speed of light c. Then we can construct another Hamiltonian

[itex] \hat{H}_2 = \frac{1}{2m} \left [\mathbf{p}+\frac{e}{c} \mathbf{A}_2(\mathbf{r}) \right ]^2[/itex]

that can be obtained from [itex] \hat{H}_1[/itex] via a gauge transformation of the vector potential

[itex] \mathbf{A}_2(\mathbf{r}) = \mathbf{A}_1(\mathbf{r}) + ∇ f(\mathbf{r}) [/itex]

with a scalar function f.

The question is now which of these two Hamiltonians do I use to evolve my initial wave function in time? I mean, if I fix the initial wave function and the Hamiltonian it is like fixing a gauge for the initial wave function.

In other words, are there some conditions that the initial wave function has to fulfill that depend on the chosen gauge?

Greetings, Syrius

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Initial wave function for an electron in a magnetic field

Loading...

Similar Threads for Initial wave function |
---|

I Difference between Schrodinger's equation and wave function? |

I Why do photons interact with e- but not with other photons? |

B What, in essence, distinguishes light from matter? |

**Physics Forums | Science Articles, Homework Help, Discussion**