I have a problem concerning gauge invariance in QM.(adsbygoogle = window.adsbygoogle || []).push({});

QM should be invariant of electromagnetic gauge. However, the following two physically equivalent vector potential:

1. [itex]A = (-\frac{1}{2}By, \frac{1}{2}Bx, 0 )[/itex]

2. [itex]A = (-By, 0 , 0 )[/itex]

generates the following hamitonian:

1. [itex]H = 1/{2M}[(P_x-\frac{eB}{2c}y)^2+(P_y+\frac{eB}{2c}x)^2 + {P_z}^2][/itex]

2. [itex]H = 1/{2M}[(P_x-\frac{eB}{2c}y)^2+{P_y}^2 + {P_z}^2][/itex]

For the first hamitonian, [itex]P_y[/itex] is a conserved quantity, but the second hamitonian yields the opposite result.

So, is [itex]P_y[/itex] conserved or not?

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# Different gauge in QM

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