MTU Cork Library Catalogue

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Quantum mechanics using computer algebra : includes sample programs for REDUCE, MAPLE, MATHEMATICA and C+ / Willi-Hans Steeb.

By: Steeb, W.-H.
Material type: materialTypeLabelBookPublisher: Singapore : World Scientific, 1994Description: viii,189 p. : ill. ; 23 cm.ISBN: 9810217706.Subject(s): Quantum theory -- Data processing | Computer algorithmsDDC classification: 530.12028553
Contents:
Conservation law and Schrodinger equation -- Wave packet and free Schrodinger equation -- Separation ansatz and Schrodinger equation -- Matrix representation in the Hilbert space -- One dimensional and trial function -- Heisenberg equation of motion -- Harmonic oscillator -- Harmonic oscillator and recursion relation -- Commutation relations of p and q -- Anharmonic oscillator -- One dimensional wkb solutions -- Angular momentum operators I -- Angular momentum operators II -- Angular momentum operators III -- Lie algebra su(3) and commutation relations -- Spin 1 lie algebra and commutation relations -- Radial symmetric potential and bound states -- Wave function of hydrogen atom I -- Wave function of hydrogen atom II -- Helium atom and trial function -- Stark effect -- Scattering in one dimension -- Gauge theory -- Driven two level system -- Free electron spin resonance -- Two point ising model with external field -- Two point Heisenberg model -- Fermi operators -- Fermi operators with spin and the Hubbard model -- Bose operators -- Matrix representation of bose operators -- Coherent states -- Quartic Hamilton operator and bose operators -- Dirac equation and dispersion law -- Perturbation theory -- Elastic scattering -- Exceptional points -- Expansion of exp(l) a exp(-l) -- Expansion of (a-b) -- Heavyside sign and delta function -- Legendre polynomials -- Laguerre polynomials -- Hermite polynomials -- Chebychev polynomials -- Spherical harmonics -- Clebsch Gordon series -- Hypergeometric functions -- Eigenvalue problems and hypergeometric differential equations -- Gamma matrices and spin matrices -- Fourier transform -- Discrete Fourier transform -- Fourier expansion -- Group theory -- Quantum groups -- Gram Schmidt orthogonalisation process -- Soliton theory and quantum mechanics -- Pade approximation -- Cumulant expansion -- Leverrier's method.
Holdings
Item type Current library Call number Copy number Status Date due Barcode Item holds
General Lending MTU Bishopstown Library Lending 530.12028553 (Browse shelf(Opens below)) 1 Available 00074862
Total holds: 0

Enhanced descriptions from Syndetics:

Solving problems in quantum mechanics is an essential skill and research activity for scientists, engineers and others. Nowadays the labor of scientific computation has been greatly eased by the advent of computer algebra packages. These do not merely perform number-crunching tasks, but enable users to manipulate algebraic expressions and equations symbolically. For example, differentiation and integration can now be carried out algebraically by the computer.This book collects standard and advanced methods in quantum mechanics and implements them using REDUCE, a popular computer algebra package. Throughout, sample programs and their output have been displayed alongside explanatory text, making the book easy to follow. Selected problems have also been implemented using two other popular packages, MATHEMATICA and MAPLE, and in the object-oriented programming language C++.Besides standard quantum mechanical techniques, modern developments in quantum theory are also covered. These include Fermi and Bose Operators, coherent states, gauge theory and quantum groups. All the special functions relevant to quantum mechanics (Hermite, Chebyshev, Legendre and more) are implemented.The level of presentation is such that one can get a sound grasp of computational techniques early on in one's scientific education. A careful balance is struck between practical computation and the underlying mathematical concepts, making the book well-suited for use with quantum mechanics courses.

Includes bibliographical references (pages 185-186) and index.

Conservation law and Schrodinger equation -- Wave packet and free Schrodinger equation -- Separation ansatz and Schrodinger equation -- Matrix representation in the Hilbert space -- One dimensional and trial function -- Heisenberg equation of motion -- Harmonic oscillator -- Harmonic oscillator and recursion relation -- Commutation relations of p and q -- Anharmonic oscillator -- One dimensional wkb solutions -- Angular momentum operators I -- Angular momentum operators II -- Angular momentum operators III -- Lie algebra su(3) and commutation relations -- Spin 1 lie algebra and commutation relations -- Radial symmetric potential and bound states -- Wave function of hydrogen atom I -- Wave function of hydrogen atom II -- Helium atom and trial function -- Stark effect -- Scattering in one dimension -- Gauge theory -- Driven two level system -- Free electron spin resonance -- Two point ising model with external field -- Two point Heisenberg model -- Fermi operators -- Fermi operators with spin and the Hubbard model -- Bose operators -- Matrix representation of bose operators -- Coherent states -- Quartic Hamilton operator and bose operators -- Dirac equation and dispersion law -- Perturbation theory -- Elastic scattering -- Exceptional points -- Expansion of exp(l) a exp(-l) -- Expansion of (a-b) -- Heavyside sign and delta function -- Legendre polynomials -- Laguerre polynomials -- Hermite polynomials -- Chebychev polynomials -- Spherical harmonics -- Clebsch Gordon series -- Hypergeometric functions -- Eigenvalue problems and hypergeometric differential equations -- Gamma matrices and spin matrices -- Fourier transform -- Discrete Fourier transform -- Fourier expansion -- Group theory -- Quantum groups -- Gram Schmidt orthogonalisation process -- Soliton theory and quantum mechanics -- Pade approximation -- Cumulant expansion -- Leverrier's method.

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