IGNOU MPH 8 SOLVED ASSIGNMENT

MPH 8: Quantum Mechanics-II

High Demand Verified Solution

★★★★★ 5/5 (870 Students)

₹80 ₹30

63% OFF You Save: ₹50

Language

Type

Session

Title Name	IGNOU MPH 8 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 8
Subject Name	Quantum Mechanics-II
Year	2026
Session	-
Language	English Medium
Assignment Code	MPH 8/Assignment-1/2026
Product Description	Assignment of MSCPH (Master of Science (Physics)) 2026. Latest MPH 08 2026 Solved Assignment Solutions
Last Date of IGNOU Assignment Submission	Last Date of Submission of IGNOU BEGC-131 (BAG) 2025-26 Assignment is for January 2026 Session: 30th September, 2026 (for December 2025 Term End Exam). Semester Wise January 2025 Session: 30th March, 2026 (for June 2026 Term End Exam). July 2025 Session: 30th September, 2025 (for December 2025 Term End Exam).
Format	Ready-to-Print PDF (.soft copy)

📅 Important Submission Dates

January 2026 Session: 31st March, 2026
July 2026 Session: 30th September, 2026

Why Choose Our Solved Assignments?

• Accuracy: Solved by IGNOU subject experts.
• Guidelines: Strictly follows 2025-26 official word limits.
• Scoring: Designed to help students achieve 90+ marks.

📋 Assignment Content Preview

Included:

MPH 8 2025 - English

Tutor Marked Assignment QUANTUM MECHANICS-II

Course Code: MPH-008

Assignment Code: MPH-008/TMA/2025

Max. Marks: 100

Note: Attempt all questions. The marks for each question are indicated against it.

PART A

1. a) Write the space translation operator in quantum mechanics ) ˆT for an infinitesimal translation (a). Hence evaluate the commutators: $[hat{x},hat{T}(a)]$ and $[hat{p}_x,hat{T}(a)]$

b) Show that for a Hamiltonian $hat{H}=frac{hat{p}_x^2}{2m}+V(x)$ to commute with the time reversal operator the potential function V(x) must be real.

2. a) Construct the wave function $psi(x_1,x_2,x_3)$ for a system of 3 identical fermions in the states $|psi_1 angle,|psi_2 angle,|psi_4 angle$ respectively of an one-dimensional box of size A

b) Calculate the ground state energy for a system of five identical spin $frac{1}{2}$ particles placed In a one-dimensional simple harmonic oscillator potential of frequency $omega _{o.}$

3. For a system of two particles each with angular momentum one $(j_1=j_2=1)$

(i) Construct the normalized states of highest and second highest J_z for total angular momentum 2.

(i) Construct the normalized state of highest J₂ for total angular momentum 1.

4. Consider the following symmetric two-dimensional infinite potential well $V(x,y)=egin{cases}0,& ext{for}0leq xleq L,0leq yleq L\infty,& ext{otherwise}end{cases}$ otherwise

Determine the first order perturbation correction to the energy eigenvalue of the two-fold degenerate first excited state, for the following perturbation: $H_1(x,y)=xy$

5. Determine the upper bound to the ground state energy for a particle in a one-dimensional box of length L. using the trial wave function: $psi(x)=x(L-x)$

PART B

6. Consider the motion of a quantum particle in a potential V(x)-ax. Use the WKB approximation to determine how the energy of the bound state E, varies with n and a for large values of n.

7. A particle is in the ground state of the simple harmonic oscillator of frequency. A t =0 frequency of the oscillator changes from particle to remain in the ground state at $omega ext{to}omega_1=3omega$ Calculate the probability for the particle to remain in the ground state at t > 0.

8. For a static (time-independent) perturbation V suddenly switched on at time t=0:

$V=egin{cases}0,&t<0\V,&t>0end{cases}$

show that the transition probability for a transition of the system from a state $|i angle$

$|n angle$ up to first order in perturbation theory is just: $=P_{i o n}=frac{4|V_{ni}|^2}{omega_{ni}^2hbar^2}sin^2left(frac{omega_{ni}t}{2} ight)$ How does the transition probability change if the time of application is doubled in the limit t→0. (6+4)

9. For a Dirac particle moving in a central potential, show that the orbital angular momentum is not a constant of motion.

$V(r)=egin{cases}-U_0,&0<r<R_0\0,&r>R_0end{cases}$

10. Consider the scattering of a particle of mass m by the following potential $V(r)=egin{cases}-U_0,&0<r<R_0\0,&r>R_0end{cases}$ Assuming that the scattering is mainly due to s-waves (1-0), calculate the s-wave phase shift.

MPH 008 (January 2026 - July 2026) - ENGLISH

Tutor Marked Assignment
QUANTUM MECHANICS-II

Course Code: MPH-008
Assignment Code: MPH-008/TMA/2026
Max. Marks: 100

Note: Attempt all questions. The marks for each question are indicated against it.

PART A

1. a) Write the space translation operator in quantum mechanics $\hat{T}(a)$ for a finite translation a along the x direction. Calculate the commutator $[\hat{x}, \hat{T}(a)]$ . You may use the Baker-Campbell-Hausdorff formula: $e^{\hat{A}} \hat{B} e^{-\hat{A}} = \hat{B} + [\hat{A}, \hat{B}] + \frac{1}{2} [\hat{A}, [\hat{A}, \hat{B}]] + \dots$

b) Consider an operator $\hat{O}$ for which $\hat{\pi}^\dagger \hat{O} \hat{\pi} = -\hat{O}$ . Show that the expectation value of $\hat{O}$ in a parity eigenstate is zero.

2. a) Determine the wave function and energy of the ground state and first excited state for a system of two identical bosons in 1D simple harmonic oscillator.

b) Define the action of the permutation operator $\hat{P}_{12}$ for a system of two particles 1 and 2 and two states $|\psi_P\rangle$ and $|\psi_{P'}\rangle$ . Show that $\hat{P}_{12}^2 = \hat{I}$ and determine the eigenvalues of $\hat{P}_{12}$ .

3. a) Write down the eigenkets $|j, m_j\rangle$ for $j = j_1 + j_2$ with $j_1 = 2; j_2 = \frac{1}{2}$ .

b) Calculate the matrix elements for J² for a system of two spin half particles.

4. Determine the first and second order perturbation correction to the ground state energy eigenvalue of the one-dimensional infinite potential well of width L ( $0 \le x \le L$ ) with the perturbation: $H_1(x) = V_0 \sin\left(\frac{\pi x}{L}\right)$ .

5. Consider the following one-dimension simple harmonic oscillator Hamiltonian operator
$$\hat{H} = -\frac{\hbar^2}{2m} \frac{d^2}{dx^2} + \frac{1}{2}m\omega^2x^2$ $
Use a trial wave function $\psi(x) = N \exp\left(-\frac{x^2}{2\alpha^2}\right)$ with a variational parameter $\alpha$ to estimate the upper bound to the ground state energy.

PART B

6. Determine the WKB approximation for the bound state energy of a particle of mass m in the potential:

$V(x) = \begin{cases} a|x| & x \geq 0 \\ 2a|x| & x < 0 \end{cases}$

7. Consider the two state problem in which the unperturbed Hamiltonian $\hat{H}_0$ has just two eigenkets, $|1\rangle$ and $|2\rangle$ with: $\hat{H}_0|1\rangle = E_1|1\rangle$ ; $\hat{H}_0|2\rangle = E_2|2\rangle$ , and E₂ > E₁. The system is subjected to a time-dependent perturbation: $\hat{V}(t) = V_0 \cos(\omega t) \left[ |1\rangle\langle2| + |2\rangle\langle1| \right]$ .
Calculate the probability for the system to be in the state $|2\rangle$ at time t, given that it is in the state $|1\rangle$ at $t = 0$ .

8. A charged particle of mass m and charge q, is confined to a one-dimensional box of side L with $0 \leq x \leq L$ . At t > 0, an electric field $\vec{E} = E_0 e^{-\alpha t} \hat{i}$ acts on the particle where $\alpha$ is a constant. If the particle is in the ground state when t < 0, calculate the probability that it will be in the first excited state for t > 0.

9. Using the Born Approximation, calculate the differential cross-section for a beam of particles of mass m scattered by a potential: $V(r) = V_0 \frac{a}{r} \exp\left( -\frac{r}{a} \right)$ . You may use:
$$\int_0^\infty e^{-\alpha x} \sin(\beta x) dx = \frac{\beta}{\alpha^2 + \beta^2} \text{ for } \alpha > 0$ $

10. a) Explain how the expression for the energy levels obtained by solving Klein Gordon equation for a Coulomb field differs from the results derived from Schrödinger equation. Why is this solution not able to explain the fine-structure splitting of the energy levels?
b) Derive the current conservation equation from the Dirac equation.

❓ Frequently Asked Questions (FAQs)

Q: How will I receive the PDF?
A: Immediately after payment, the download link will appear.

Q: Is this hand-written or typed?
A: This is a professional typed computer PDF. You can use it as a reference for your handwritten submission.

➕Other Details

Details

Latest IGNOU Solved Assignment
IGNOU MPH 8 2026 Solved Assignment
IGNOU 2026 Solved Assignment
IGNOU MSCPH Master of Science (Physics) 2026 Solved Assignment
IGNOU MPH 8 Quantum Mechanics-II 2026 Solved Assignment

Looking for IGNOU MPH 8 Solved Assignment 2026. You are on the Right Website. We provide Help book of Solved Assignment of MSCPH MPH 8 - Quantum Mechanics-IIof year 2026 of very low price.
If you want this Help Book of IGNOU MPH 8 2026 Simply Call Us @ 9199852182 / 9852900088 or you can whatsApp Us @ 9199852182

IGNOU MSCPH Assignments Jan - July 2026 - 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.

Download a PDF soft copy of IGNOU MPH 8 Quantum Mechanics-II MSCPH Latest Solved Assignment for Session January 2026 - December 2026 in English Language.

If you are searching out Ignou MSCPH MPH 8 solved assignment? So this platform is the high-quality platform for Ignou MSCPH MPH 8 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 8 Quantum Mechanics-II course offered by IGNOU for the year 2026.Are you a student of high IGNOU looking for high quality and accurate IGNOU MPH 8 Solved Assignment 2026 English Medium?

Students who are searching for IGNOU Master of Science (Physics) (MSCPH) Solved Assignments 2026 at low cost. We provide all Solved Assignments, Project reports for Masters & Bachelor students for IGNOU. Get better grades with our assignments! ensuring that our IGNOU Master of Science (Physics) Solved Assignment meet the highest standards of quality and accuracy.Here you will find some assignment solutions for IGNOU MSCPH Courses that you can download and look at. All assignments provided here have been solved.IGNOU MPH 8 SOLVED ASSIGNMENT 2026. Title Name MPH 8 English Solved Assignment 2026. Service Type Solved Assignment (Soft copy/PDF).

Are you an IGNOU student who wants to download IGNOU Solved Assignment 2024? IGNOU Solved Assignment 2023-24 Session. IGNOU Solved Assignment and In this post, we will provide you with all solved assignments.

If you’ve arrived at this page, you’re looking for a free PDF download of the IGNOU MSCPH Solved Assignment 2026. MSCPH is for Master of Science (Physics).

IGNOU solved assignments are a set of questions or tasks that students must complete and submit to their respective study centers. The solved assignments are provided by IGNOU Academy and must be completed by the students themselves.

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

IGNOU MPH 8 Solved Assignment

ignou assignment 2026, 2026 MPH 8

IGNOU MPH 8 Assignment

ignou solved assignment MPH 8

MPH 8 Assignment 2026

solved assignment MPH 8

MPH 8 Assignment 2026

assignment of ignou MPH 8

Download IGNOU MPH 8 Solved Assignment 2026

ignou assignments MPH 8

Ignou result MPH 8

Ignou Assignment Solution MPH 8

Get the full solved PDF Now

Why Choose IGNOU Academy for Your Assignments?

Getting your assignments right is the first step toward a successful degree. At IGNOU Academy, we provide high-quality reference materials designed to simplify your academic journey. Here is why thousands of students trust us:

Latest Curriculum: All content is strictly based on the current IGNOU syllabus.
Perfect Formatting: Understand the ideal structure and layout to score better marks.
Concept Clarity: We break down complex topics into simple, easy-to-grasp explanations.
Exam-Ready: Our materials serve as excellent revision notes for your term-end exams.
Student-Centric Language: Written in clear, simple English/Hindi to ensure every learner understands.
Nationwide Trust: A preferred choice for IGNOU learners across India.

Disclaimer: These materials are intended as reference study guides to help you understand topics and formats. We encourage students to use these insights to prepare and write their own original assignments as per university guidelines.

How to Get Your Solved Assignment PDF

Visit Us: Go to www.ignouacademy.com.
Find Your Course: Search for your specific program and subject code.
Select the Session: Choose the latest reference guide for the current academic session.
Quick Checkout: Add to your cart, log in (or register quickly), and complete your purchase.
Instant Access: Download your study material directly from your account after payment.

Step-by-Step: Downloading Official Question Papers

Visit www.ignouacademy.com.
Click on the "IGNOU Assignment Question Papers" section.
Filter by your Course, Session, and Medium (English/Hindi).
Download the PDF directly to your device.

How to Submit Your IGNOU Assignments

Handwritten is Key: Use clean A4-size sheets and write neatly.
The Front Page: Ensure your first page clearly mentions your Name, Enrollment Number, Course Code, Subject, and Study Center Code.
Offline Submission: Visit your assigned Study Center, submit in person, and always collect your acknowledgment receipt.
Online Submission: If your center allows, scan each subject as a separate PDF. Submit via the official Google Form, Email, or Portal provided by your center. Keep a screenshot of the confirmation.

Tracking Your Submission Status

Want to know if your marks are updated?

Visit the Student Zone on the official IGNOU website.
Navigate to "Assignment Status."
Enter your Enrollment Number and Program Code.
View your submission dates, current status, and any remarks from the evaluator.

A Quick Tip for Success

Dear Students, remember that assignments carry 30% weightage in your final result. They aren't just a formality—they are a game-changer for your overall percentage. Regular study and timely submission are the keys to a high grade.

Success in IGNOU = Smart Study + Well-Prepared Assignments!

Need Help? Contact IGNOU Academy WhatsApp: +91 9199852182 Website: www.ignouacademy.com

IGNOU Solved Assignments Assignments Ignou Projects Project Previous Year Solved Exam Papers Notes Notes Sample Question Papers Sample Question Papers