Examveda

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, R_z is the matrix corresponding to rotation about the Z-axis. The conserved quantities are (the symbols have their usual meaning)

A. p_x, p_z, L_z

B. p_x, p_y, L_z, E

C. p_y, L_z, E

D. p_y, p_z, L_x, E

Answer: Option B

This Question Belongs to Engineering Physics >> Quantum Mechanics

Join The Discussion

Related Questions on Quantum Mechanics

A particle is placed in a one-dimensional box of size L along the X-axis, (0 < x < L). Which of the following is true?

A. In the ground state, the probability of finding the particle in the interval $$\left( {\frac{L}{4},\,\frac{{3L}}{4}} \right)$$ is half

B. In the first excited state, the probability of finding the particle in the interval $$\left( {\frac{L}{4},\,\frac{{3L}}{4}} \right)$$ is half This also holds for states with n = 4, 6, 8, . . . .

C. For an arbitrary state $$\left| \psi \right\rangle ,$$ the probability of finding the particle in the left half of the well is half

D. In the ground state, the particle has a definite momentum

View Answer

If the probability that x lies between x and x + dx is P(x) dx = ae^-ax dx, where 0 < x < $$\infty $$ , a > 0, then the probability that x lies between x₁ and x₂ (x₂ > x₁) is

A. (e^-ax₁ - e^-ax₂)

B. a(e^-ax₁ - e^-ax₂)

C. e^-ax₂ (e^-ax₁ - e^-ax₂)

D. None of the above

View Answer

A Michelson interferometer is illuminated with monochromatic light. When one of the mirrors is moved through a distance of 25.3 μm, 92 fringes pass through the cross-wire. The wavelength of the monochromatic light is

A. 500 nm

B. 550 nm

C. 600 nm

D. 650 nm

View Answer

An electron is in a statewith spin wavefunction \[{\phi _s} = \left[ {\begin{array}{*{20}{c}} {\frac{{\sqrt 3 }}{2}} \\ {\frac{1}{2}} \end{array}} \right]\] in the s_z representation. What is the probability of, finding the z-component of its spin along the $$ - {\bf{\hat Z}}$$ direction?

A. 0.75

B. 0.50

C. 0.35

D. 0.25

View Answer

A classical particle is moving in an external potential field V(x...

Join The Discussion

Read More: MCQ Type Questions and Answers