Back-of-the-Envelope Quantum Mechanics

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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 textboo…

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    Om Back-of-the-Envelope Quantum Mechanics

    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.Contents:Ground State Energy of a Hybrid Harmonic-Quartic Oscillator: A Case StudyBohr-Sommerfeld Quantization“Halved” Harmonic Oscillator: A Case StudySemi-Classical Matrix Elements of Observables and Perturbation TheoryVariational ProblemsGravitational Well: A Case StudyMiscellaneousThe Hellmann-Feynman TheoremLocal Density Approximation TheoriesIntegrable Partial Differential EquationsReadership: Advanced undergraduate and beginning graduate students in physics.

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    Detaljer

    Format
    E-Bok
    Filformat
    PDF
    Utgivelsesår
    2013
    Forlag
    World Scientific Publishing Co
    Språk
    Engelsk
    ISBN
    9789814508476
    Sider
    172

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