Vidyalelo
Engineering Physics · Q61

Quantum Mechanics

Engineering and GATE · Engineering Physics · question 61

Q61

A classical particle is moving in an external potential field V(x, y, z) which is invariant under the following infinitesimal transformations \[ array*20c x x'& = &x + x \\ y y'& = &y + y \\ [ array*20c x \\ y array ] [ array*20c x' \\ y' array ]& = &R_z [ array*20c x \\ y array ] array\] where, Rz is the matrix corresponding to rotation about the Z-axis. The conserved quantities are (the symbols have their usual meaning)

A classical particle is moving in an external potential field V(x, y, z) which is invariant under the following infinitesimal transformations
\begin{array}{*{20}{c}} {x \to x'}& = &{x + \delta x} \\ {y \to y'}& = &{y + \delta y} \\ {\left[ {\begin{array}{*{20}{c}} x \\ y \end{array}} \right] \to \left[ {\begin{array}{*{20}{c}} {x'} \\ {y'} \end{array}} \right]}& = &{{R_z}\left[ {\begin{array}{*{20}{c}} x \\ y \end{array}} \right]} \end{array}
where, Rz is the matrix corresponding to rotation about the Z-axis. The conserved quantities are (the symbols have their usual meaning)
A.
px, pz, Lz
B.
px, py, Lz, E
Answer
C.
py, Lz, E
D.
py, pz, Lx, E

Answer: Option B

Solution

Answer: Option B
No explanation is given for this question Let's Discuss on Board