IGNOU MPH 4 SOLVED ASSIGNMENT

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IGNOU MPH 4 SOLVED ASSIGNMENT

~~Rs. 90~~
Rs. 15

IGNOU MPH 4 SOLVED ASSIGNMENT

~~Rs. 90~~
Rs. 15

Last Date of Submission of IGNOU MPH-04 (MSCPH) 2026 Assignment is for January 2026 Session: 30th September, 2026 (for December 2026 Term End Exam).
Semester Wise
January 2026 Session: 30th March, 2026 (for June 2026 Term End Exam).
July 2026 Session: 30th September, 2026 (for December 2026 Term End Exam).

Title Name	IGNOU MPH 4 SOLVED ASSIGNMENT
Type	Soft Copy (E-Assignment) .pdf
University	IGNOU
Degree	MASTER DEGREE PROGRAMMES
Course Code	MSCPH
Course Name	Master of Science (Physics)
Subject Code	MPH 4
Subject Name	Quantum Mechanics-I
Year	2026
Session
Language	English Medium
Assignment Code	MPH-04/Assignmentt-1//2026
Product Description	Assignment of MSCPH (Master of Science (Physics)) 2026. Latest MPH 04 2026 Solved Assignment Solutions
Last Date of IGNOU Assignment Submission	Last Date of Submission of IGNOU MPH-04 (MSCPH) 2026 Assignment is for January 2026 Session: 30th September, 2026 (for December 2026 Term End Exam). Semester Wise January 2026 Session: 30th March, 2026 (for June 2026 Term End Exam). July 2026 Session: 30th September, 2026 (for December 2026 Term End Exam).

~~Rs. 90~~
Rs. 15

Questions Included in this Help Book

Ques 1.

Electrons are accelerated through a potential 150 V and incident on a crystal with interatomic spacing $d = 0.20\text{ nm}$ . Calculate the de Broglie wavelength and the first-order Bragg diffraction angle.

Ques 2.

Estimate the uncertainty in the energy of a photon localized within a distance of $0.1\text{ nm}$ .

Ques 3.

i) Normalize the wave function:
$$\psi(x,0) = N \left[ \sin\left( \frac{\pi x}{L} \right) + \sin\left( \frac{2\pi x}{L} \right) \right], 0 \le x < L.$

ii) Calculate the expectation value of x for a particle in this state.

Ques 4.

A quantum mechanical particle in one dimension has the wave function:

$$\psi(x) = Nx^n : x > 0 ; n > 1.$

Use the Schrödinger equation to determine the corresponding potential V(x).

Ques 5.

A 1.5 mA beam of electrons enters a sharply defined boundary with a velocity $3.0 \times 10^6\text{ ms}^{-1}$ , and then its velocity reduces to $2.0 \times 10^6\text{ ms}^{-1}$ , due to the difference in potential. Calculate the transmitted and reflected currents.

Ques 6.

Show that for any stationary state of a symmetric potential well: $\langle x^2 \rangle \ne 0$ .

Ques 7.

Calculate the expectation value of the potential energy for the first excited state of a simple harmonic oscillator.

Ques 8.

i) Write down the eigenfunctions for the $\psi_{300}$ and $\psi_{310}$ states of the hydrogen atom.
ii) Write the eigenvalues of $\hat{L}^2$ and $\hat{L}_z$ for the states $\psi_{300}$ and $\psi_{310}$ .
iii) Calculate the most probable value of r for the hydrogen atom in the state $\psi_{210}$ .

Ques 9.

Consider the following state vectors: $|\psi\rangle = \begin{pmatrix} 1 \\ i \\ -1 \end{pmatrix}; |\phi\rangle = \begin{pmatrix} 2 \\ 1-i \\ i \end{pmatrix}$ .

Calculate (i) the norm of $|\psi\rangle$ and (ii) the inner product $\langle\psi|\phi\rangle$ .

Ques 10.

If an operator $\hat{O}$ is Hermitian and an operator $\hat{U}$ is unitary, show that the operator $\hat{U}\hat{O}\hat{U}^{-1}$ is Hermitian.

Ques 11.

The spectral representation of an operator $\hat{\Omega}$ in a two-dimensional orthonormal basis $|\phi_1\rangle,|\phi_2\rangle$ is

$$\hat{\Omega} = 3|\phi_1\rangle\langle\phi_1| + \sqrt{2}|\phi_1\rangle\langle\phi_2| + \sqrt{2}|\phi_2\rangle\langle\phi_1| + 2|\phi_2\rangle\langle\phi_2|$

Determine the matrix elements of $\Omega$ .

Ques 12.

$|1\rangle$ and $|2\rangle$ are the orthonormal basis states of a two-dimensional Hilbert space. A Hermitian operator $\hat{A}$ in this basis is given by the spectral representation: $\hat{A} = 3|1\rangle\langle1| - 1|2\rangle\langle2|$ . For a normalized state given by

$$|\psi\rangle = \frac{1}{2}|1\rangle + \frac{\sqrt{3}}{2}|2\rangle, \text{ calculate } \langle\hat{A}\rangle \text{ and the root mean square deviation in } \hat{A} .$

Ques 13.

Derive the Heisenberg equations of motion for $\hat{S}_x$ and $\hat{S}_y$ for the Hamiltonian $\hat{H} = \omega\hat{S}_z$ .

Ques 14.

For the simple harmonic oscillator
i) Show that $[\hat{H}, \hat{a}] = -\hbar\omega\hat{a}$ .
ii) Calculate the matrix element $\langle n|\hat{x}|n + 1\rangle$

Ques 15.

i) Write down the angular momentum states $|j, m_j\rangle$ and calculate the matrix elements of $\hat{J}_x, \hat{J}_y$ and $\hat{J}_z$ for $j = 1/2$ .
ii) For the angular momentum state $|3,1\rangle$ show that $J_+|3,1\rangle = \hbar\sqrt{10}|3,2\rangle$ and $J_-|3,1\rangle = 2\hbar\sqrt{3}|3,0\rangle$ .

Ques 16.

Show that in the terms of the $|\uparrow\rangle$ and $|\downarrow\rangle$ basis vectors defined by
$\hat{S}_z|\uparrow\rangle = \frac{\hbar}{2}|\uparrow\rangle$ ; $\hat{S}_z|\downarrow\rangle = -\frac{\hbar}{2}|\downarrow\rangle$ , we can write: $\hat{S}_x = \frac{\hbar}{2} \left[ |\uparrow\rangle\langle\downarrow| + |\downarrow\rangle\langle\uparrow| \right]$

Ques 17.

Ques 18.

Estimate the uncertainty in the energy of a photon localized within a distance of $0.1\text{ nm}$ .

Ques 19.

i) Normalize the wave function:
$$\psi(x,0) = N \left[ \sin\left( \frac{\pi x}{L} \right) + \sin\left( \frac{2\pi x}{L} \right) \right], 0 \le x < L.$

ii) Calculate the expectation value of x for a particle in this state.

Ques 20.

A quantum mechanical particle in one dimension has the wave function:

$$\psi(x) = Nx^n : x > 0 ; n > 1.$

Use the Schrödinger equation to determine the corresponding potential V(x).

Ques 21.

Ques 22.

Show that for any stationary state of a symmetric potential well: $\langle x^2 \rangle \ne 0$ .

Ques 23.

Calculate the expectation value of the potential energy for the first excited state of a simple harmonic oscillator.

Ques 24.

Ques 25.

Consider the following state vectors: $|\psi\rangle = \begin{pmatrix} 1 \\ i \\ -1 \end{pmatrix}; |\phi\rangle = \begin{pmatrix} 2 \\ 1-i \\ i \end{pmatrix}$ .

Calculate (i) the norm of $|\psi\rangle$ and (ii) the inner product $\langle\psi|\phi\rangle$ .

Ques 26.

If an operator $\hat{O}$ is Hermitian and an operator $\hat{U}$ is unitary, show that the operator $\hat{U}\hat{O}\hat{U}^{-1}$ is Hermitian.

Ques 27.

The spectral representation of an operator $\hat{\Omega}$ in a two-dimensional orthonormal basis $|\phi_1\rangle,|\phi_2\rangle$ is

$$\hat{\Omega} = 3|\phi_1\rangle\langle\phi_1| + \sqrt{2}|\phi_1\rangle\langle\phi_2| + \sqrt{2}|\phi_2\rangle\langle\phi_1| + 2|\phi_2\rangle\langle\phi_2|$

Determine the matrix elements of $\Omega$ .

Ques 28.

$$|\psi\rangle = \frac{1}{2}|1\rangle + \frac{\sqrt{3}}{2}|2\rangle, \text{ calculate } \langle\hat{A}\rangle \text{ and the root mean square deviation in } \hat{A} .$

Ques 29.

Derive the Heisenberg equations of motion for $\hat{S}_x$ and $\hat{S}_y$ for the Hamiltonian $\hat{H} = \omega\hat{S}_z$ .

Ques 30.

For the simple harmonic oscillator
i) Show that $[\hat{H}, \hat{a}] = -\hbar\omega\hat{a}$ .
ii) Calculate the matrix element $\langle n|\hat{x}|n + 1\rangle$

Ques 31.

Ques 32.

~~Rs. 90~~
Rs. 15

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IGNOU MSCPH Assignments Jan - July 2025 - IGNOU University has uploaded its current session Assignment of the MSCPH Programme for the session year 2026. Students of the MSCPH Programme can now download Assignment questions from this page. Candidates have to compulsory download those assignments to get a permit of attending the Term End Exam of the IGNOU MSCPH Programme.

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If you are searching out Ignou MSCPH MPH 4 solved assignment? So this platform is the high-quality platform for Ignou MSCPH MPH 4 solved assignment. Solved Assignment Soft Copy & Hard Copy. We will try to solve all the problems related to your Assignment. All the questions were answered as per the guidelines. The goal of IGNOU Solution is democratizing higher education by taking education to the doorsteps of the learners and providing access to high quality material. Get the solved assignment for MPH 4 Quantum Mechanics-I course offered by IGNOU for the year 2026.Are you a student of high IGNOU looking for high quality and accurate IGNOU MPH 4 Solved Assignment 2026 English Medium?

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Course Name	Master of Science (Physics)
Course Code	MSCPH
Programm	MASTER DEGREE PROGRAMMES Courses
Language	English

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