AMP STUDY NOTES
PHY3708 · ATOMIC & NUCLEAR PHYSICS
Complete Module
Additional Practice Problems
All five chapters' practice problems combined into a single volume, in
order, with complete step-by-step solutions.
Chapter 1 — Elements of Quantum Mechanics
Chapter 2 — Basic Nuclear Properties
Chapter 3 — Nuclear Models
Chapter 4 — Radioactive Decay
Chapter 5 — Nuclear Reactions
ADDITIONAL PRACTICE PROBLEMS · 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
Additional Practice Problems
Seven further practice problems spanning the full chapter —
hydrogen-like wave function construction, spherical harmonics,
infinite well superpositions, the kinetic-energy operator, associated
Laguerre polynomial construction, the Hermite equation, and the
delta-function potential — each with a complete, independently
worked step-by-step solution.
PRACTICE PROBLEMS · CHAPTER 1
Independent study material. These problems are independently written, in the style and difficulty range typical of
this module's assessments, but are original variations — not reproductions of any specific examination,
assignment, or textbook problem — with independently worked solutions. Not affiliated with, endorsed by, or
sourced from the University of South Africa (UNISA) or any official assessment body. © AMP Study Notes.
, AMP Study Notes — PHY3708 — Chapter 1
Chapter 1: Additional Practice Problems
WHAT THIS SET COVERS
• Hydrogen-like wave function construction and nodes, • Associated Laguerre polynomial construction as a
for two different states not used in the main chapter standalone skill
notes
• The Hermite equation for a higher oscillator level
• Spherical harmonic construction by hand at
• A quantitative probability calculation for the delta-
• A second infinite-well superposition, and a second function potential
kinetic-energy-operator eigenfunction problem
Use this set after working through the main chapter notes and the worked examples there. Each problem below targets a different
state, quantum number, or skill than the main Study Notes document, so working through both gives broader coverage than either
alone.
Problem 1: Hydrogen-like 3p State — Radial Function and Node
Problem. For the 3p state of a singly-ionized helium ion He ( , so ), construct the
radial wave function up to normalization, and find the radius at which it has a node.
Step 1 — identify the required Laguerre polynomial. "3p" means , so and
: the radial function has the form , with .
Step 2 — construct . Using with (so ),
and :
Step 3 — solve for the node. Setting : . Converting to using
with :
Step 4 — check against the node-counting rule. A hydrogen-like radial function has exactly
nodes; here , matching the single root found — a quick and worthwhile
consistency check any time this construction is carried out.
Page 2 of 7
PHY3708 · ATOMIC & NUCLEAR PHYSICS
Complete Module
Additional Practice Problems
All five chapters' practice problems combined into a single volume, in
order, with complete step-by-step solutions.
Chapter 1 — Elements of Quantum Mechanics
Chapter 2 — Basic Nuclear Properties
Chapter 3 — Nuclear Models
Chapter 4 — Radioactive Decay
Chapter 5 — Nuclear Reactions
ADDITIONAL PRACTICE PROBLEMS · 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
Additional Practice Problems
Seven further practice problems spanning the full chapter —
hydrogen-like wave function construction, spherical harmonics,
infinite well superpositions, the kinetic-energy operator, associated
Laguerre polynomial construction, the Hermite equation, and the
delta-function potential — each with a complete, independently
worked step-by-step solution.
PRACTICE PROBLEMS · CHAPTER 1
Independent study material. These problems are independently written, in the style and difficulty range typical of
this module's assessments, but are original variations — not reproductions of any specific examination,
assignment, or textbook problem — with independently worked solutions. Not affiliated with, endorsed by, or
sourced from the University of South Africa (UNISA) or any official assessment body. © AMP Study Notes.
, AMP Study Notes — PHY3708 — Chapter 1
Chapter 1: Additional Practice Problems
WHAT THIS SET COVERS
• Hydrogen-like wave function construction and nodes, • Associated Laguerre polynomial construction as a
for two different states not used in the main chapter standalone skill
notes
• The Hermite equation for a higher oscillator level
• Spherical harmonic construction by hand at
• A quantitative probability calculation for the delta-
• A second infinite-well superposition, and a second function potential
kinetic-energy-operator eigenfunction problem
Use this set after working through the main chapter notes and the worked examples there. Each problem below targets a different
state, quantum number, or skill than the main Study Notes document, so working through both gives broader coverage than either
alone.
Problem 1: Hydrogen-like 3p State — Radial Function and Node
Problem. For the 3p state of a singly-ionized helium ion He ( , so ), construct the
radial wave function up to normalization, and find the radius at which it has a node.
Step 1 — identify the required Laguerre polynomial. "3p" means , so and
: the radial function has the form , with .
Step 2 — construct . Using with (so ),
and :
Step 3 — solve for the node. Setting : . Converting to using
with :
Step 4 — check against the node-counting rule. A hydrogen-like radial function has exactly
nodes; here , matching the single root found — a quick and worthwhile
consistency check any time this construction is carried out.
Page 2 of 7
