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*Multiple options can be correct

QUESTION: 1

Which of the following correspond to the possible states of a hydrogen atom with *n* = 2. (States are designated as ψ_{nlm}.)

Solution:

The correct answers are:

*Multiple options can be correct

QUESTION: 2

For particle in a 3** d** box of length

Solution:

The correct answers are: (** n_{x}, n_{y}, n_{z}**) taking values 1, 1, 5, (

*Multiple options can be correct

QUESTION: 3

For a particle in a 3 dimensional box

Solution:

Second excited state

3 fold degenerate!

The correct answers are: Ground state energy is non zero, The second excited state is 3 fold degenerate

*Multiple options can be correct

QUESTION: 4

Consider an atomic electron in the l = 3 state. If L is the magnitude of the angular momentum, L_{z} is its z component, θ is the angle makes with the z axis then :

Solution:

** l** = 3

The correct answer is:

*Multiple options can be correct

QUESTION: 5

For a quantum harmonic oscillator in 3 dimensions

Solution:

(0, 0, 3) → 3 state

(1, 1, 1) → 1 state

(0, 1, 2) → 6 state

∴ 3 + 1 + 6 = 10 fold degenerate.

The correct answers are: The ground state is non degenerate, The third excited state is 10 fold degenerate

*Multiple options can be correct

QUESTION: 6

Consider the case of a 3 dimensional harmonic oscillator. Choose the correct statement.

Solution:

can be degenerate

No symmetry in potential. Energy levels cannot be degenerate. Both have zero point energy.

The correct answers are: In case of an isotropic harmonic oscillator, the energy levels can be degenerate, In case of an anisotropic oscillator, there is no degeneracy since the potential is not symmetric, Both isotropic and anisotropic oscillators have zero point energy

*Multiple options can be correct

QUESTION: 7

Select the correct statements about the uncertainty principle in 3 dimensions

Solution:

Uncertainty in x = Δx

Uncertainty in p_{x} = Δp_{x}

Uncertainty principle in *x*-direction,

Uncertainty principle in *y*-direction,

Uncertainty principle in *z*-direction,

No relation between Δx and Δp_{y} and so on.

The correct answers are: No restriction on and and so on

*Multiple options can be correct

QUESTION: 8

Consider the case of particle in a 3** d** box and a 3

Solution:

(For Harmonic Oscillator)

The correct answers are: The energy of the ground state of a 3** d** harmonic oscillator is zero., The ground state energy of 3

*Multiple options can be correct

QUESTION: 9

For a particle in 3 dimensional box

Solution:

The correct answers are: The number of quantum numbers is equal to dimensions of potential distribution, The symmetry of box leads to degeneracy, The spin quantum number does not arise from Schrodinger wave equations, If we consider spin also for fermions then the degeneracy of energy levels become twice

*Multiple options can be correct

QUESTION: 10

For a rectangular 3 dimensional box

Solution:

For a 3** d** box with different edge length (a

ψ will be different even if different combination gives the same value of E

The correct answers are: Degenerate energy levels have different wave functions, Degenerate energy levels have same parity

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