Difference Between Landau & Symmetric Gauges for Magnetic Fields

[raintrek]

Could anybody explain to me the difference between a Landau Gauge and Symmetric Gauge?

I know the Landau Gauge is given by A = (0,Bx,0) producing a constant magnetic field in the z direction. I am *assuming* (process of elimination!) that A = ½B × r = (-yB/2,xB/2,0) is an example of a symmetric gauge which, likewise, corresponds to a constant z magnetic field.

I'm really after some clarification in terms of how the gauge chosen for a magnetic field affects the Schrödinger equation for a charged particle. If anyone could point me in the right direction I'd be very grateful! Thanks in advance.

 

[Astronuc]

Some relevant discussions:

https://en.wikipedia.org/wiki/Landau_quantization Comment:

There is some gauge freedom in the choice of vector potential for a given magnetic field. The Hamiltonian is gauge invariant, which means that adding the gradient of a scalar field to  changes the overall phase of the wave function by an amount corresponding to the scalar field. But physical properties are not influenced by the specific choice of gauge.

https://courses.physics.illinois.edu/phys581/sp2013/charge_mag.pdf

https://par.nsf.gov/servlets/purl/10187378