Back-of-the-envelope Quantum Mechanics: With Extensions To Many-body Systems, Integrable Pdes, And Rare And Exotic Methods
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A01=Maxim Olchanyi (Olshanii)
Author_Maxim Olchanyi (Olshanii)
Back-of-the-Envelope
Bethe Ansatz
Bohlin-Arnold-Vassiliev Map
BohlinAcAEURA"ArnoldAcAEURA"Vassiliev Map
Bohr-Sommerfeld Quantization
BohrAcAEURA"Sommerfeld Quantization
Breathers
Calculus of Variations
Calogero Model
Category=PHQ
Category=UYX
Circle Inversion
Dimensional Analysis
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Hellmann-Feynman Theorem
HellmannAcAEURA"Feynman Theorem
Integrable Nonlinear Partial Differential Equations
Kadomtsev-Petviashvili Equation
KadomtsevAcAEURA"Petviashvili Equation
Korteweg-de Vries Equation
Lieb-Liniger Model
LiebAcAEURA"Liniger Model
Nonlinear SchrAfA?dinger Equation
Nonlinear Schrodinger Equation
Order of Magnitude
Perturbation Theory
Power Index Method
QM-SUSY
Quantum Mechanics
Self-Similarity
Semi-Classical
Sine-Gordon Equation
SineAcAEURA"Gordon Equation
Solitons
Virial Theorem
WKB
Product details
- ISBN 9789819820405
- Publication Date: 14 Feb 2024
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Paperback
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Dimensional and order-of-magnitude estimates are practiced by almost everybody but taught almost nowhere. When physics students engage in their first theoretical research project, they soon learn that exactly solvable problems belong only to textbooks, that numerical models are long and resource consuming, and that "something else" is needed to quickly gain insight into the system they are going to study. Qualitative methods are this "something else", but typically, students have never heard of them before.The aim of this book is to teach the craft of qualitative analysis using a set of problems, some with solutions and some without, in advanced undergraduate and beginning graduate Quantum Mechanics. Examples include a dimensional analysis solution for the spectrum of a quartic oscillator, simple WKB formulas for the matrix elements of a coordinate in a gravitational well, and a three-line-long estimate for the ionization energy of atoms uniformly valid across the whole periodic table. The pièce de résistance in the collection is a series of dimensional analysis questions in Integrable Nonlinear Partial Differential Equations with no dimensions existing a priori. Solved problems include the relationship between the size and the speed of solitons of the Korteweg-de Vries equation and an expression for the oscillation period of a Nonlinear Schrödinger breather as a function of its width.A new theme that appears in the second edition are the rare and exotic methods in elementary quantum mechanics. The new chapter covers quantum-mechanical supersymmetry, power index method, scale invariance, self-similarity, and circle inversion.
