AMP STUDY NOTES
PHY3708 · ATOMIC & NUCLEAR PHYSICS
Complete Module
Study Notes
All five chapters combined into a single volume, in order, for the full
module.
Chapter 1 — Elements of Quantum Mechanics
Chapter 2 — Basic Nuclear Properties
Chapter 3 — Nuclear Models
Chapter 4 — Radioactive Decay
Chapter 5 — Nuclear Reactions
STUDY NOTES · ALL CHAPTERS
Independent study material. These notes are an independently authored revision aid covering the full PHY3708
module and on general patterns observed in how this material tends to be assessed. They are not affiliated with,
endorsed by, or sourced from the University of South Africa (UNISA) or any off
,AMP STUDY NOTES
PHY3708 · ATOMIC & NUCLEAR PHYSICS
Chapter 1
Elements of Quantum
Mechanics
Exam-focused study notes: the wave function and expectation
values, the time-independent Schrödinger equation and its standard
1D solutions, three-dimensional quantum mechanics, and fully
worked practice problems with complete step-by-step solutions.
STUDY NOTES · CHAPTER 1
Independent study material. These notes are an independently authored revision aid based on standard non-
relativistic quantum mechanics (following the treatment in Griffiths & Schroeter, Introduction to Quantum
Mechanics) and on general patterns observed in how this material tends to be assessed. They are not affiliated
with, endorsed by, or sourced from the University of South Africa (UNISA) or any official assessment body, and all
practice problems are original variations written for study purposes, with independently worked solutions. © AMP
Study Notes.
, AMP Study Notes — PHY3708 — Chapter 1
Chapter 1: Elements of Quantum Mechanics
TOPICS COVERED IN THIS CHAPTER
• The wave function, normalization, and expectation • The delta-function potential and the finite potential
values of position, momentum, and general well
observables
• Vector-space formalism: kets, inner products, and
• The time-independent Schrödinger equation and linear transformations (background)
stationary states
• Separating the 3D Schrödinger equation: the radial
• The infinite potential well and superpositions of its equation, the centrifugal barrier, and spherical
eigenstates harmonics
• The quantum harmonic oscillator and the • The hydrogen atom: wave functions, energy levels,
dimensionless-variable reduction to the Hermite and finding nodes
equation
PHY3708 Atomic and Nuclear Physics (Unisa). This chapter is the module's compressed tour
through non-relativistic quantum mechanics, before the course turns to nuclei from Chapter 2 onward.
Based on a review of how this material tends to be assessed, the recurring high-yield tasks are: the
harmonic-oscillator dimensionless-variable derivation reducing the Schrödinger equation to the
Hermite equation; constructing a hydrogen-like wave function's radial and angular parts for a named
state and finding its nodes; and applying the kinetic-energy operator to a piecewise-defined 1D wave
function to extract a normalization constant and an expectation value. The abstract vector-space
"Formalism" material is covered only briefly below, as background — it rarely appears directly in
assessment.
Page 2 of 17
, AMP Study Notes — PHY3708 — Chapter 1
What is Most Examined?
HIGH-YIELD TASK HOW IT TENDS TO APPEAR PRIORITY
Harmonic oscillator Introduce the dimensionless variable , reduce the Very high
derivation Schrödinger equation, and derive the resulting Hermite equation and
quantized energies — a frequently examined, fully-derivable question
type.
Hydrogen-like wave Given , build the explicit radial and Very high
function construction angular pieces for a named state and find where the wave function has
nodes. A frequently recurring problem type.
Kinetic-energy operator Apply to a given piecewise , then compute the High
on a 1D wave function normalization constant and .
Separating the 3D Show splits the equation into a radial and an angular High
Schrödinger equation piece, and that substituting gives a 1D-like radial
equation with a centrifugal term.
Associated Legendre Construct and from their defining formulas for a Medium-
polynomials / spherical given . high
harmonics by hand
Infinite well Given as a sum of box eigenstates, find the allowed energies, Medium
superposition states their probabilities, and .
Delta-function potential Quote the single bound-state wave function and binding energy, and use Low-
it in a simple probability calculation. medium
Page 3 of 17
PHY3708 · ATOMIC & NUCLEAR PHYSICS
Complete Module
Study Notes
All five chapters combined into a single volume, in order, for the full
module.
Chapter 1 — Elements of Quantum Mechanics
Chapter 2 — Basic Nuclear Properties
Chapter 3 — Nuclear Models
Chapter 4 — Radioactive Decay
Chapter 5 — Nuclear Reactions
STUDY NOTES · ALL CHAPTERS
Independent study material. These notes are an independently authored revision aid covering the full PHY3708
module and on general patterns observed in how this material tends to be assessed. They are not affiliated with,
endorsed by, or sourced from the University of South Africa (UNISA) or any off
,AMP STUDY NOTES
PHY3708 · ATOMIC & NUCLEAR PHYSICS
Chapter 1
Elements of Quantum
Mechanics
Exam-focused study notes: the wave function and expectation
values, the time-independent Schrödinger equation and its standard
1D solutions, three-dimensional quantum mechanics, and fully
worked practice problems with complete step-by-step solutions.
STUDY NOTES · CHAPTER 1
Independent study material. These notes are an independently authored revision aid based on standard non-
relativistic quantum mechanics (following the treatment in Griffiths & Schroeter, Introduction to Quantum
Mechanics) and on general patterns observed in how this material tends to be assessed. They are not affiliated
with, endorsed by, or sourced from the University of South Africa (UNISA) or any official assessment body, and all
practice problems are original variations written for study purposes, with independently worked solutions. © AMP
Study Notes.
, AMP Study Notes — PHY3708 — Chapter 1
Chapter 1: Elements of Quantum Mechanics
TOPICS COVERED IN THIS CHAPTER
• The wave function, normalization, and expectation • The delta-function potential and the finite potential
values of position, momentum, and general well
observables
• Vector-space formalism: kets, inner products, and
• The time-independent Schrödinger equation and linear transformations (background)
stationary states
• Separating the 3D Schrödinger equation: the radial
• The infinite potential well and superpositions of its equation, the centrifugal barrier, and spherical
eigenstates harmonics
• The quantum harmonic oscillator and the • The hydrogen atom: wave functions, energy levels,
dimensionless-variable reduction to the Hermite and finding nodes
equation
PHY3708 Atomic and Nuclear Physics (Unisa). This chapter is the module's compressed tour
through non-relativistic quantum mechanics, before the course turns to nuclei from Chapter 2 onward.
Based on a review of how this material tends to be assessed, the recurring high-yield tasks are: the
harmonic-oscillator dimensionless-variable derivation reducing the Schrödinger equation to the
Hermite equation; constructing a hydrogen-like wave function's radial and angular parts for a named
state and finding its nodes; and applying the kinetic-energy operator to a piecewise-defined 1D wave
function to extract a normalization constant and an expectation value. The abstract vector-space
"Formalism" material is covered only briefly below, as background — it rarely appears directly in
assessment.
Page 2 of 17
, AMP Study Notes — PHY3708 — Chapter 1
What is Most Examined?
HIGH-YIELD TASK HOW IT TENDS TO APPEAR PRIORITY
Harmonic oscillator Introduce the dimensionless variable , reduce the Very high
derivation Schrödinger equation, and derive the resulting Hermite equation and
quantized energies — a frequently examined, fully-derivable question
type.
Hydrogen-like wave Given , build the explicit radial and Very high
function construction angular pieces for a named state and find where the wave function has
nodes. A frequently recurring problem type.
Kinetic-energy operator Apply to a given piecewise , then compute the High
on a 1D wave function normalization constant and .
Separating the 3D Show splits the equation into a radial and an angular High
Schrödinger equation piece, and that substituting gives a 1D-like radial
equation with a centrifugal term.
Associated Legendre Construct and from their defining formulas for a Medium-
polynomials / spherical given . high
harmonics by hand
Infinite well Given as a sum of box eigenstates, find the allowed energies, Medium
superposition states their probabilities, and .
Delta-function potential Quote the single bound-state wave function and binding energy, and use Low-
it in a simple probability calculation. medium
Page 3 of 17
