Quantum Mechanics MCQs Question and Answer in Engineering Physics

A. $$\left( {n + \frac{1}{2}} \right)\hbar \omega $$

B. $$\left( {2n + \frac{1}{2}} \right)\hbar \omega $$

C. $$\left( {2n + \frac{3}{2}} \right)\hbar \omega $$

D. $$\left( {n + \frac{3}{2}} \right)\hbar \omega $$

A. $$i\hbar \frac{d}{{dx}}$$

B. $$ - i\hbar \frac{d}{{dx}}$$

C. $$i\hbar \frac{\partial }{{\partial t}}$$

D. $$ - \frac{{{h^2}}}{{2m}}\frac{{{d^2}}}{{d{x^2}}}$$

A. $${\bf{\hat B}}$$ is Hermitian

B. $${\bf{\hat B}}$$ is anti-Hermitian

C. $${\bf{\hat B}}$$ is Hermitian and $${\bf{\hat A}}$$ and $${\bf{\hat B}}$$ commute

D. $${\bf{\hat B}}$$ is Hermitian and $${\bf{\hat A}}$$ and $${\bf{\hat B}}$$ anti-commute

A. E⁽¹⁾ = 0; E⁽²⁾ < 0

B. E⁽¹⁾ > 0; E⁽²⁾ = 0

C. E⁽¹⁾ = 0; E⁽²⁾ depends on the sign of V₀

D. E⁽¹⁾ < 0; E⁽²⁾ < 0

A. decaying, oscillatory

B. oscillatory, oscillatory

C. oscillatory, decaying

D. decaying, decaying

A. A₀e^2x

B. A₀ cosh 2x

C. A₀e^-2x

D. A₀ sinh 2x

A. 4

B. 6

C. 8

D. 10

A. 4

B. 9

C. 13

D. Infinitely many

A. $$\frac{2}{L}\sin \left( {\frac{{n\pi x}}{L}} \right)\cos \left( {\frac{{m\pi y}}{L}} \right)$$

B. $$\frac{2}{L}\cos \left( {\frac{{l\pi x}}{L}} \right)\cos \left( {\frac{{n\pi y}}{L}} \right)$$

C. $$\frac{2}{L}\sin \left( {\frac{{m\pi x}}{L}} \right)\sin \left( {\frac{{n\pi y}}{L}} \right)$$

D. $$\frac{2}{L}\cos \left( {\frac{{n\pi x}}{L}} \right)\sin \left( {\frac{{l\pi y}}{L}} \right)$$

A. This is an eigen state of both energy and momentum

B. This is an eigen state of momentum and not energy

C. This is an eigen state of energy and not momentum

D. This is not an eigen state of energy or momentum