Quantum Mechanics I Quiz

Which of the following bra and ket relations is correct

• 
• 
• 
• None of the above

An operator A is said to be hermitian if

• A^ϯ = A

• A^ϯ = - A

• A^ϯ = - A^*

• All of the above

Which of the following is conserved under invariant of rotational transformation

• total energy of the system

• linear momentum of the system

• angular momentum of the system

• time

The commutation relation of A and B is

• [A,B] = AB - BA

• [A,B] = BA - AB

• [A,B] = AB + BA

• None of the above

Which of the following is correct

• p_x = i ħ

• p_x = - i ħ ∂/∂x

• px = i ħ ∂/∂x

• None of the above

The potential energy of a one dimensional harmonic oscillator is

• ½ k x

• ½ k x²

• ½ k² x

• None of the above

The value of m and l in spherical harmonic solution is

• m = 0, 1, 2 …. l, and l = 0, ±1, ±2 …

• m = 0, ±1, ±2 …. ±l, and l = 0, 1, 2, …

• m = 0, 1, 2 …. l, and l = 0, 1, 2, …

• None of the above

The angular momentum commutation relation is

• [L_x, L_y] = i ħ L_z

• [L_x, L_y] = - i ħ L_z

• [L_x, L_y] = i ħ L_x

• None of the above

Which of the following relation is correct

• [L_z,L₊] = i ħ L₊

• [L_z,L₊] = ħ L₊

• [L_z,L₊] = ħ L_z

• None of the above

The energy of a free particle in 3-D box of size 'a' is

• h²/2ma² (n_x² +n_y² + n_z²)

• h²/4ma² (n_x² +n_y² + n_z²)

• h²/6ma² (n_x² +n_y² + n_z²6

• h²/8ma² (n_x² +n_y² + n_z²)