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|a 2013937175
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|a 016488175
|2 Uk
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|a 9781461471158 (acidfree paper)
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|a 146147115X (acidfree paper)
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|a 9781461471165
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|a (OCoLC)ocn828487961
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|a BTCTA
|b eng
|c BTCTA
|e rda
|d YDXCP
|d CSA
|d OHX
|d TXA
|d OCLCQ
|d UKMGB
|d STF
|d HEBIS
|d IQU
|d PUL
|d OCLCF
|d IXA
|d DLC
|d BD-DhAAL
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|a pcc
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|a QC174.12
|b .H346 2013
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|a QA
|2 lcco
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|a 530.12
|2 22
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| 100 |
1 |
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|a Hall, Brian C.,
|e author.
|9 21848
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| 245 |
1 |
0 |
|a Quantum theory for mathematicians /
|c Brian C. Hall.
|
| 260 |
|
|
|a New York :
|b Springer,
|c 2013.
|
| 300 |
|
|
|a xvi, 554 pages :
|b illustrations ;
|c 24 cm
|
| 490 |
1 |
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|a Graduate texts in mathematics,
|x 0072-5285 ;
|v 267
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| 504 |
|
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|a Includes bibliographical references (pages 545-548) and index.
|
| 505 |
0 |
0 |
|t The experimental origins of quantum mechanics:
|t Is light a wave or a particle? ;
|t Is an electron a wave or a particle? ;
|t Schrödinger and Heisenberg ;
|t A matter of interpretation ;
|g Exercises --
|t A first approach to classical mechanics:
|t Motion in R¹ ;
|t Motion in R[superscript n] ;
|t Systems of particles ;
|t Angular momentum ;
|t Poisson brackets and Hamiltonian mechanics ;
|t The Kepler problem and the Runge-Lenz vector ;
|g Exercises --
|t First approach to quantum mechanics:
|t Waves, particles, and probabilities ;
|t A few words about operators and their adjoints ;
|t Position and the position operator ;
|t Momentum and the momentum operator ;
|t The position and momentum operators ;
|t Axioms of quantum mechanics : operators and measurements ;
|t Time-evolution in quantum theory ;
|t The Heisenberg picture ;
|t Example : a particle in a box ;
|t Quantum mechanics for a particle in R [superscript n] ;
|t Systems of multiple particles ;
|t Physics notation ;
|g Exercises --
|t The free Schrödinger equation:
|t Solution by means of the Fourier transform ;
|t Solution as a convolution ;
|t Propagation of the wave packet : first approach ;
|t Propagation of the wave packet : second approach ;
|t Spread of the wave packet ;
|g Exercises --
|t Particle in a square well:
|t The time-independent Schrödinger equation ;
|t Domain questions and the matching conditions ;
|t Finding square-integrable solutions ;
|t Tunneling and the classically forbidden region ;
|t Discrete and continuous spectrum ;
|g Exercises --
|t Perspectives on the spectral theorem:
|t The difficulties with the infinite-dimensional case ;
|t The goals of spectral theory ;
|t A guide to reading ;
|t The position operator ;
|t Multiplication operators ;
|t The momentum operator --
|t The spectral theorem for bounded self-adjoint operators : statements:
|t Elementary properties of bounded operators ;
|t Spectral theorem for bounded self-adjoint operators, I ;
|t Spectral theorem for bounded self-adjoint operators, II ;
|g Exercises --
|t The spectral theorem for bounded self-adjoint operators : proofs:
|t Proof of the spectral theorem, first version ;
|t Proof of the spectral theorem, second version ;
|g Exercises --
|t Unbounded self-adjoint operators:
|g Introduction ;
|t Adjoint and closure of an unbounded operator ;
|t Elementary properties of adjoints and closed operators ;
|t The spectrum of an unbounded operator ;
|t Conditions for self-adjointness and essential self-adjointness ;
|t A counterexample ;
|t An example ;
|t The basic operators of quantum mechanics ;
|t Sums of self-adjoint operators ;
|t Another counterexample ;
|g Exercises --
|t The spectral theorem for unbounded self-adjoint operators:
|t Statements of the spectral theorem ;
|t Stone's theorem and one-parameter unitary groups ;
|t The spectral theorem for bounded normal operators ;
|t Proof of the spectral theorem for unbounded self-adjoint operators ;
|g Exercises --
|t The harmonic oscillator:
|t The role of the harmonic oscillator ;
|t The algebraic approach ;
|t The analytic approach ;
|t Domain conditions and completeness ;
|g Exercises --
|t The uncertainty principle:
|t Uncertainty principle, first version ;
|t A counterexample ;
|t Uncertainty principle, second version ;
|t Minimum uncertainty states ;
|g Exercises --
|t Quantization schemes for Euclidean space:
|t Ordering ambiguities ;
|t Some common quantization schemes ;
|t The Weyl quantization for R²[superscript n] ;
|t The "No go" theorem of Groenewold ;
|g Exercises --
|t The Stone-Von Neumann theorem:
|t A heuristic argument ;
|t The exponentiated commutation relations ;
|t The theorem ;
|t The Segal-Bargmann space ;
|g Exercises --
|t The WKB approximation:
|g Introduction ;
|t The old quantum theory and the Bohr-Sommerfeld condition ;
|t Classical and semiclassical approximations ;
|t The WKB approximation away from the turning points ;
|t The Airy function and the connection formulas ;
|t A rigorous error estimate ;
|t Other approaches ;
|g Exercises --
|t Lie groups, Lie algebras, and representations:
|g Summary ;
|t Matrix Lie groups ;
|t Lie algebras ;
|t The matrix exponential ;
|t The Lie algebra of a matrix Lie group ;
|t Relationships between Lie groups and Lie algebras ;
|t Finite-dimensional representations of Lie groups and Lie algebras ;
|t New representations from old ;
|t Infinite-dimensional unitary representations ;
|g Exercises --
|t Angular momentum and spin:
|t The role of angular momentum in quantum mechanics ;
|t The angular momentum operators in R³ ;
|t Angular momentum from the Lie algebra point of view ;
|t The irreducible representations of so(3) ;
|t The irreducible representations of SO(3) ;
|t Realizing the representations inside L²(S²) --
|t Realizing the representations inside L²(M³) ;
|t Spin ;
|t Tensor products of representations : "addition of angular momentum" ;
|t Vectors and vector operators ;
|g Exercises --
|t Radial potentials and the hydrogen atom:
|t Radial potentials ;
|t The hydrogen atom : preliminaries ;
|t The bound states of the hydrogen atom ;
|t The Runge-Lenz vector in the quantum Kepler problem ;
|t The role of spin ;
|t Runge-Lenz calculations ;
|g Exercises --
|t Systems and subsystems, multiple particles:
|g Introduction ;
|t Trace-class and Hilbert-Schmidt operators ;
|t Density matrices : the general notion of the state of a quantum system ;
|t Modified axioms for quantum mechanics ;
|t Composite systems and the tensor product ;
|t Multiple particles : bosons and fermions ;
|t "Statistics" and the Pauli exclusion principle ;
|g Exercises --
|t The path integral formulation of quantum mechanics:
|t Trotter product formula ;
|t Formal derivation of the Feynman path integral ;
|t The imaginary-time calculation ;
|t The Wiener measure ;
|t The Feynman-Kac formula ;
|t Path integrals in quantum field theory ;
|g Exercises --
|t Hamiltonian mechanics on manifolds:
|t Calculus on manifolds ;
|t Mechanics on symplectic manifolds ;
|g Exercises --
|t Geometric quantization on Euclidean space:
|g Introduction ;
|t Prequantization ;
|t Problems with prequantization ;
|t Quantization ;
|t Quantization of observables ;
|g Exercises --
|t Geometric quantization on manifolds:
|g Introduction ;
|t Line bundles and connections ;
|t Prequantization ;
|t Polarizations ;
|t Quantization without half-forms ;
|t Quantization with half-forms : the real case ;
|t Quantization with half-forms : the complex case ;
|t Pairing maps ;
|g Exercises --
|t A review of basic material:
|t Tensor products of vector spaces ;
|t Measure theory ;
|t Elementary functional analysis ;
|t Hilbert spaces and operators on them.
|
| 526 |
|
|
|a CSE
|x Sowmitra Das
Lecturer,
Department of Computer Science
Course name : Quantum Computing I (CSE 481)
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| 541 |
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|a Book Finder International.
|c 44097
|
| 650 |
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0 |
|a Quantum theory
|x Mathematics.
|9 39415
|
| 650 |
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0 |
|a Quantum theory.
|
| 650 |
|
0 |
|a Mathematical physics.
|
| 650 |
|
0 |
|a Computer science.
|
| 830 |
|
0 |
|a Graduate texts in mathematics,
|x 0072-5285 ;
|v 267.
|
| 942 |
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|g 5535.00
|l 0
|o 530.12 HAL
|p 3010044097
|r 2025-02-04
|t 1
|v 5535.00
|w 2025-02-04
|y BK
|x Requisitioned by Sowmitra Das for the course named- ''Quantum Computing I (CSE 481)''.
|