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Previous year question hub

Quantum Principles and Exactly Solvable Potentials - Quantum Mechanics - Physics Previous Year Questions

Practice Quantum Principles and Exactly Solvable Potentials - Quantum Mechanics - Physics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

20Papers
20Years
116Questions
1Topics

Quantum Principles and Exactly Solvable Potentials question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Quantum Principles and Exactly Solvable Potentials. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Easy 59 50.9%
Medium 56 48.3%
Hard 1 0.9%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

MCQ 89 76.7%
Numerical Answer Type (NAT) 17 14.7%
MSQ 8 6.9%
Fill in the blanks 2 1.7%

Subject weightage

Top subjects by unique question coverage.

Physics
116 Qs

Most asked topics

Top topics across the included previous year papers.

Quantum Mechanics
116 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Quantum Principles and Exactly Solvable Potentials
116 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

Physics (PH) 2026
6 Qs
Physics (PH) 2025
6 Qs
Physics (PH) 2024
4 Qs
Physics (PH) 2023
4 Qs
Physics (PH) 2022
7 Qs
Physics (PH) 2021
5 Qs
Physics (PH) 2020
3 Qs
Physics (PH) 2019
6 Qs
Physics (PH) 2018
2 Qs
Physics (PH) 2017
7 Qs
Physics (PH) 2016
7 Qs
Physics (PH) 2015
3 Qs
Physics (PH) 2014
3 Qs
Physics (PH) 2013
4 Qs
Physics (PH) 2012
6 Qs
Physics (PH) 2011
8 Qs
Physics (PH) 2010
3 Qs
Physics (PH) 2009
7 Qs
Physics (PH) 2008
6 Qs
Physics (PH) 2007
19 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
Physics (PH) 202620266View paper
Physics (PH) 202520256View paper
Physics (PH) 202420244View paper
Physics (PH) 202320234View paper
Physics (PH) 202220227View paper
Physics (PH) 202120215View paper
Physics (PH) 202020203View paper
Physics (PH) 201920196View paper
Physics (PH) 201820182View paper
Physics (PH) 201720177View paper
Physics (PH) 201620167View paper
Physics (PH) 201520153View paper
Physics (PH) 201420143View paper
Physics (PH) 201320134View paper
Physics (PH) 201220126View paper
Physics (PH) 201120118View paper
Physics (PH) 201020103View paper
Physics (PH) 200920097View paper
Physics (PH) 200820086View paper
Physics (PH) 2007200719View paper

All Quantum Principles and Exactly Solvable Potentials previous year questions

Practice every matching question in batches of 20, with every available option.

1
2007 · Physics · Quantum Mechanics · Quantum Principles and Exactly Solvable Potentials
Physics (PH) 2007
The wavefunction of a particle, moving in a one-dimensional time-independent potential V(x), is given by ψ(x) = e^{-ax^2 + bx}, where a and b are constants. This means that the potential V(x) is of the form
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2
2007 · Physics · Quantum Mechanics · Quantum Principles and Exactly Solvable Potentials
Physics (PH) 2007
The wavefunction of a particle, moving in a one-dimensional time-independent potential \(V(x)\), is given by \(\psi(x) = e^{-ax^2}\), where \(a\) and \(b\) are constants. This means that the potential \(V(x)\) is of the form
Open complete paper
3
2007 · Physics · Quantum Mechanics · Quantum Principles and Exactly Solvable Potentials
Physics (PH) 2007
A particle with energy \(E\) is in a time-independent double well potential as shown in the figure.
Which of the following statements about the particle is NOT correct?
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4
2007 · Physics · Quantum Mechanics · Quantum Principles and Exactly Solvable Potentials
Physics (PH) 2007
The energy levels of a particle of mass \(m\) in a potential of the form \(V(x) = \infty, x \leq 0\)
\(\qquad\qquad\quad = \frac{1}{2} m \omega^2 x^2, x > 0\)
are given, in terms of quantum number \(n = 0,1,2,3,...\), by
Open complete paper
5
2007 · Physics · Quantum Mechanics · Quantum Principles and Exactly Solvable Potentials
Physics (PH) 2007
The energy levels of a particle of mass \(m\) in a potential of the form \(V(x) = \infty, x \le 0\) \(= \frac{1}{2} m \omega^2 x^2, x > 0\) are given, in terms of quantum number \(n = 0,1,2,3,...\), by
Open complete paper
6
2007 · Physics · Quantum Mechanics · Quantum Principles and Exactly Solvable Potentials
Physics (PH) 2007
For a particle of mass \( m \) in a one-dimensional harmonic oscillator potential of the form \( V(x) = \frac{1}{2} m \omega^2 x^2 \), the first excited energy eigenstate is \( \psi(x) = x e^{-\alpha x^2} \). The value of \( \alpha \) is
Open complete paper
7
2007 · Physics · Quantum Mechanics · Quantum Principles and Exactly Solvable Potentials
Physics (PH) 2007
If \( [x, p] = i\hbar \), the value of \( [x^3, p] \) is
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8
2007 · Physics · Quantum Mechanics · Quantum Principles and Exactly Solvable Potentials
Physics (PH) 2007
For a particle of mass \( m \) in a one-dimensional harmonic oscillator potential of the form \( V(x) = \frac{1}{2} m \omega^2 x^2 \), the first excited energy eigenstate is \( \psi(x) = x e^{-a x^2} \). The value of \( a \) is
Open complete paper
9
2007 · Physics · Quantum Mechanics · Quantum Principles and Exactly Solvable Potentials
Physics (PH) 2007
There are only three bound states for a particle of mass \( m \) in a one-dimensional potential well of the form shown in the figure. The depth \( V_0 \) of the potential satisfies
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10
2007 · Physics · Quantum Mechanics · Quantum Principles and Exactly Solvable Potentials
Physics (PH) 2007
Three operators \( X, Y \) and \( Z \) satisfy the commutation relations \( [X, Y] = i\hbar Z \), \( [Y, Z] = i\hbar X \) and \( [Z, X] = i\hbar Y \). The set of all possible eigenvalues of the operator \( Z \), in units of \( \hbar \), is
Open complete paper
11
2007 · Physics · Quantum Mechanics · Quantum Principles and Exactly Solvable Potentials
Physics (PH) 2007
The normalization factor \( \psi_0 \) of this wavefunction is
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12
2007 · Physics · Quantum Mechanics · Quantum Principles and Exactly Solvable Potentials
Physics (PH) 2007
The energy eigenvalue corresponding to this state is
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13
2007 · Physics · Quantum Mechanics · Quantum Principles and Exactly Solvable Potentials
Physics (PH) 2007
The expectation value of \( p^2 \) ( \( p \) is the momentum operator) in this state is
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14
2007 · Physics · Quantum Mechanics · Quantum Principles and Exactly Solvable Potentials
Physics (PH) 2007

The normalization factor \(\psi_0\) of this wavefunction is

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15
2007 · Physics · Quantum Mechanics · Quantum Principles and Exactly Solvable Potentials
Physics (PH) 2007

The expectation value of \(p^2\) ( \(p\) is the momentum operator) in this state is

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16
2008 · Physics · Quantum Mechanics · Quantum Principles and Exactly Solvable Potentials
Physics (PH) 2008
For a physical system, two observables \(O_1\) and \(O_2\) are known to be compatible. Choose the correct implication from amongst those given below:
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17
2008 · Physics · Quantum Mechanics · Quantum Principles and Exactly Solvable Potentials
Physics (PH) 2008
An exact measurement of the position of a simple harmonic oscillator (SHO) is made with the result \(x = x_0\). [The SHO has energy levels \(E_n (n = 0, 1, 2, ...)\) and associated normalized wavefunctions \(\psi_n\). Subsequently, an exact measurement of energy \(E\) is made. Using the general notation \(Pr(E = E')\) denoting the probability that a result \(E'\) is obtained for this measurement, the following statements are written. Which one of the following statements is correct?
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18
2008 · Physics · Quantum Mechanics · Quantum Principles and Exactly Solvable Potentials
Physics (PH) 2008
A particle is placed in a one dimensional box of size \( L \) along the x-axis (\(0
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19
2008 · Physics · Quantum Mechanics · Quantum Principles and Exactly Solvable Potentials
Physics (PH) 2008
Throughout \( 0 < x < L \), the wave-function
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20
2008 · Physics · Quantum Mechanics · Quantum Principles and Exactly Solvable Potentials
Physics (PH) 2008
Let the probability current associated with the incident wave be $S_0$. Let $R$ be the reflection coefficient. Then
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Showing 20 of 111 questions