IGNOU MPH 11 2026 - The Hamiltonian for the non-relativistic, non-interacting, monoa

Question

The Hamiltonian for the non-relativistic, non-interacting, monoatomic ideal gas is given by

$$H(q, p) = \sum_{i=1}^{3N} \frac{p_i^2}{2m} + U(q_i)$

where m is the mass of the particle and U(q_i) is the potential energy. Obtain an expression of the phase space volume of the energy shell and hence obtain an expression of number of microstates.

19 Jan 2026

Answer :

Word Count : 262

The Hamiltonian of a non-relativistic, non-interacting, monoatomic ideal gas is [ H(q,p) = \sum_{i=1}^{3N} \frac{p_i^2}{2m} + U(q_i), ] where (p_i) are the momenta, (q_i) are the positions, and (U(q_i)) is the potential energy. The phase space volume corresponding to energies less than or equal to (E) is defined as [ \Omega(E) = \frac{1}{h^{3N}} \int \cdots \int \mathrm{d}^{3N}q , \mathrm{d}^{3N}p ; \Theta(E - H(q,p)), ] where (\Theta) is the

___ ______ ________ _____ ____ _______ ______ _______.
________ ___ _________ _____ ________ _____ ___ ________ _____ ______ ____ ________.
__________ ____ __________ ___ _____ _____ _______ _______ ____ ____ _____.
_________ ___ _____ _________ ________ _______ ____.
__________ ________ ______ ______ _____ ____ ____ _______ ____.
___ ___ __________ ___ _____ __________ _________ ________ ________ _____.
___ ____ ____ ______ __________ _____ ______ ______ ________.
__________ _______ ____ _____ _______ ________ ____ _________ ________ _________ ________.
_____ _________ ________ _______ _____ ___ ________ __________ ________.
___ ____ _______ ________ ______.
________ __________ __________ _______ ________ ____ ___ ___ _____.
___ __________ ______ ___ _____ _______ __________ _______.
___ ___ ___ __________ __________ ____ ___.
__________ ___ ________ ___ ______.
_____ _______ ____ ________ ________ ___ ______ ________ ______ _____ ________ ________.
____ ________ _________ _______ _________ ____ ______ ____.
______ _____ _______ ____ _____ _______.
_________ ____ _____ ____ _______ _________ ____ _______ _________ __________ ____ ________.
________ _________ _____ _______ ______.
________ __________ ______ __________ _______ ________ ________ _________ ______.
__________ ____ ______ _____ ____ _____ _______ ________.
______ __________ ___ _____ _____ _______.
___ ________ ______ ________ __________ _____ ___.
______.

IGNOU ACADEMY

Your IGNOU journey, made easier.

Solved Assignments
Study Notes
Guess Papers
Question Papers

Call Us WhatsApp

STUDY • PREPARE • SUCCEED

Skip in 10

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