CML1001 Common Quiz-1 February 5, 2026
Total marks = 35, Total time = 45 min
Name:
Entry No.:
Fill in the Blanks (2 marks/question)
.
1. The dimension of a normalized wavefunction for a particle in a 2D box is
2. For a particle-in-a-1D-box with infinitely high walls and length L in a state with eight equally probable
maxima, the quantum number is n =
, the normalized wavefunction is ψ(x) =
,
and the probability in 3L/4 ≤ x ≤ L is
. [0.5 + 0.5 + 1]
3. For simple harmonic oscillator having a potential 21 kx2 :
(a) The Schrödinger equation is
(b) The commutator [x, px ] is
4. For a two-particle system,
RR
ψ ∗ (x1 , x2 )ψ(x1 , x2 ) dx1 dx2 represents
5. For a particle in 1D potential V (x),
surement of position and energy because
commutators].
.
uncertainty exists in simultaneous mea[justify your answer using
6. Electrons with λ = 0.30 nm have energy E =
J.
7. The observed absorption maxima of cyanine cations, (3HC)2 N+ = CH − (CH = CH)k − N(:)(CH3 )2 , are
given below:
k
N
Color
0
1
2
3
4
5
6
4
6
8
10
12
14
16
Colorless
Colorless
Yellow
Red
Blue
Green
Colorless
For cyanine dyes with L = 2(k + 2)d0 , d0 = 140 pm:
(a) The calculated λ for k = 0 is
nm
(b) Color variation (observed above) occurs because
1
8. The expectation value ⟨x2 ⟩ for a wavefunction ψ(x) can be obtained using
9. For Hamiltonian eigenfunction ψ with eigenvalue α, α must be
q
.
and
.
2
a sin(πx/a) sin(2πy/a) is
.
11. The Schrödinger equation for earth (mass m) in sun’s gravitational field is
.
10. Energy of particle in square box (a×a) in state
12. For ψ = √13 ψ1 +
q
2
3 ψ2 :
(a) P (E1 ) =
(b) ⟨E 2 ⟩ =
13. For  = x̂ + ip̂x and † = x̂ − ip̂x :
in terms of  and †
(a) x̂2 =
(b) [Â, † ] =
14. For ground state of particle in 3D box, ⟨px ⟩ =
because
.
True or False (Circle T or F). 1 mark/question
15. T
F
For non-interacting particles i and j, the wavefunction is ψ = ψi + ψj .
16. T
F
The operator  + iÊ is Hermitian if both  and Ê are Hermitian.
17. T
F
The function exp(−|x|) (−∞ ≤ x ≤ ∞) is an acceptable quantum mechanical wavefunction.
18. T
F
Wave-particle duality sets fundamental limits on information obtainable about quantum systems.
19. T
F
For solutions y1 , y2 of the wave equation, ysum = ay1 + by2 is also a solution.
20. T
F
The quantum mechanical kinetic energy is
21. T
F
⟨x2 ⟩ is always greater than ⟨x⟩2 .
2
R∞ h
i
ℏ2 k2 ∂ 2
∗ Ψ) dx.
−
(Ψ
2
2m ∂x
−∞