- Start by reviewing the fundamental mathematical concepts such as calculus, linear algebra, and differential equations.
- Familiarize yourself with important mathematical operations like differentiation, integration, matrix operations, and solving differential equations.
- Ensure a clear understanding of trigonometric functions, complex numbers, and vector algebra.


- Brush up on the mathematical foundation of quantum mechanics, including the postulates and principles.
- Understand the concept of wave-particle duality and the mathematical representation of wavefunctions.
- Revise the Schrödinger equation and its solutions, including time-independent and time-dependent formulations.
- Practice solving problems related to the quantum mechanical operators such as position, momentum, and energy.


- Review the mathematical representation of atomic structure, including the Bohr model and the quantum mechanical model.
- Understand the mathematical formulation of atomic orbitals and electron configurations.
- Study the mathematical description of atomic spectra and transition probabilities.


- Familiarize yourself with the mathematical aspects of molecular structure, including molecular orbitals and electronic configurations.
- Review the mathematical methods used to calculate molecular properties such as bond lengths, bond angles, and molecular energies.
- Understand the mathematical representation of molecular symmetry and its applications.


- Solve a variety of numerical problems and exercises related to atomic and molecular physics.
- Work on previous year question papers and sample papers to get an idea of the types of mathematical problems asked in the UPSC Physics Optional exam.
- Practice solving problems under time constraints to improve speed and accuracy.


- Utilize textbooks, lecture notes, and other study materials to supplement your understanding of mathematical formalism in atomic and molecular physics.
- Join online forums or study groups to discuss and clarify doubts with fellow aspirants or experts in the field.
- Make use of online educational platforms like EduRev for comprehensive study materials and practice questions.

By following these steps, you can effectively revise the mathematical formalism in atomic and molecular physics for the UPSC Physics Optional exam. Remember to allocate sufficient time for practice and revision to strengthen your understanding of the subject.