Prerequisites: Self-Assessment

This textbook assumes the following background. Use this self-assessment to identify areas you may need to review before beginning.

Physics Prerequisites

Introductory Physics (Required)

You should be comfortable with: - Newton's laws, conservation of energy and momentum - Electrostatics: Coulomb's law, electric potential, capacitance - Magnetism: magnetic force on charged particles, Faraday's law - Waves: wave equation, superposition, interference, standing waves

Self-test: Can you solve a two-body elastic collision in the center-of-mass frame? Can you calculate the electric potential energy of two point charges?

Modern Physics / Introductory Quantum Mechanics (Required)

You should be comfortable with: - Wave-particle duality, de Broglie wavelength - The Schrödinger equation (time-independent) for simple potentials - Quantum numbers (n, l, m_l, m_s) for the hydrogen atom - Spin and the Pauli exclusion principle - Basic concepts: superposition, probability amplitude, expectation value

Self-test: Can you write down the time-independent Schrödinger equation for a particle in a finite square well? Can you explain what the quantum numbers of the hydrogen atom represent?

Special Relativity (Required)

You should be comfortable with: - Lorentz factor $\gamma = 1/\sqrt{1 - v^2/c^2}$ - Relativistic energy: $E = \gamma mc^2$, rest energy $E_0 = mc^2$ - Relativistic energy-momentum relation: $E^2 = (pc)^2 + (mc^2)^2$ - Four-momentum and invariant mass

Self-test: A proton has kinetic energy $T = 500$ MeV. What is its total energy? Its momentum? (Proton rest energy: 938.3 MeV.)

Mathematics Prerequisites

Calculus (Required)

  • Multivariable calculus: partial derivatives, gradient, divergence, curl
  • Integration in multiple dimensions (spherical coordinates especially)
  • Ordinary differential equations (first and second order, constant coefficients)

Linear Algebra (Required)

  • Vectors and matrices, eigenvalues and eigenvectors
  • Basis vectors, inner products, orthogonality
  • Diagonalization of matrices

Additional Mathematics (Helpful but Reviewed in Text)

The following topics are used in this book but are reviewed when introduced: - Spherical harmonics (Chapter 5, Appendix A) - Angular momentum coupling and Clebsch-Gordan coefficients (Chapter 5) - Fourier transforms (Chapter 9) - Complex analysis basics (Chapter 18, resonance theory) - Probability and statistics (Chapter 12, decay statistics)

Computational Prerequisites

For the Progressive Project (Nuclear Data Analysis Toolkit): - Basic Python programming (variables, functions, loops, arrays) - Familiarity with numpy arrays and matplotlib plotting - No advanced programming experience required — all code is explained

If you have not used Python before, we recommend completing a basic Python tutorial before attempting the Project Checkpoints. The code is supplementary — you can learn all the physics without writing any code.

What You Do NOT Need

  • No prior nuclear physics. This book starts from the discovery of the nucleus and builds everything from there.
  • No quantum field theory. Where QFT concepts appear (beta decay, QCD), they are introduced at the level needed.
  • No advanced mathematical physics. Bessel functions, Legendre polynomials, and other special functions are introduced in context and summarized in Appendix A.
  • No laboratory experience. Experimental techniques are described conceptually. (But if your university offers a nuclear physics laboratory course, take it.)