Harish Parthasarathy | Category: Physics

Binding Type: Hard Binding

Book Details

ISBN: 9789388342216

YOP: 2019

Pages: 520

Order also onThis is a book about all the mathematical aspects of wave motion including the fundamental equations governing sound waves in a pipe, waves in the sea, electromagnetic waves with applications to geometrical optics and diffraction theory, gravitational waves as predicted by Einstein’s general theory of relativity, quantum mechanical waves, namely the dynamics of the wave function arising in Schrodinger’s wave equation for atomic systems both without and with noise. It also includes the general theory of lenses and prisms. A separate section of the book includes some general aspects of probability and random processes both from classical and quantum probabilistic angle. This section has been written keeping in mind general aspects of filtering theory wherein one proposes to estimate wave motion dynamics from noisy measurements. Electromagnetic waves inside confined walls like waveguides and cavity resonators are also dealt with in some detail. The book will be useful to undergraduate and postgraduate students of physics, applied mathematics and electronics and communication engineering. The sections dealing with quantum probability and quantum filtering will be useful to the advanced researcher in applied mathematics as well as to researchers in quantum optics. Each chapter of the book has four sections, one summary, two technical discussion, three points to remember and four exercises. This makes the material easy to understand for even an undergraduate student of physics.

1.The Definition of a propagating wave in one, two and three dimensions.

2.Standing waves in one, two and three dimensions.

3.The polarization of a wave.

4.The wave equation in one, two and three dimensions.

One dimensional waves in a vibrating string.

Two dimensional waves in a vibrating membrane.

Three dimensional waves in optics.

5.The polarization of a wave.

6.Basics of fluid dynamics.

7.Waves in a fluid–derivation from first principles

8.Longitudinal sound/pressure waves in a tube.

9.The difference between transverse and longitudinal waves in terms of wave

polarization.

10. Maxwell’s equations and the wave equation for the electric and magnetic

fields in free space.

11. Solution to Maxwell’s equations in terms of retarded potentials satisfying

the wave equation with source.

12. The principle of superposition.

13. Diffraction and interference of waves.

14. Green’s function for wave equation with sources–Fraunhoffer and Fresnel’s

diffraction.

15.The basic Eikonal equation of geometric optics.

16.Describing the trajectory of light in a medium having spatially varying

refractive index.

17. Propagation of light in anisotropic, inhomogeneous and time varying

medium

18. The Schrodinger wave equation in quantum mechanics

19. The effect of noise on the Schrodinger wave equation–Open systems, ie,

coupling of the system to the bath environment.

20. Wave equation with random non-uniform refractive index.

21. The relationship between the wave equation and the Helmholtz equation

for waves of given frequency

22. Waves in a confined region.

23. Schrodinger’s wave equation for mixed states in the position kernel

domain.

24. Gravitational waves in flat space-time and curved space-time background.

25. Quantum gravity, the canonical ADM formalism-Schrodinger’s equation

for the wave function of the space-time metric.

26. Plasma waves.

27. Evans-Hudson diffusion as a quantum mechanical generalization of the

wave equation with noise.

28. Waves in an expanding universe–Newtonian theory of small fluctuations

and general relativistic theory of small fluctuations.

29. EM waves in a curved space-time geometry with inhomogeneous permittivitypermeability

tensor.

30. Quantum Optics. Here, the photon field is a quantum electromagneticfield expressible as a superposition of annihilation and creation operators of the photon field with the coefficients of the linear combination being positions of

time and space.

31. Quantum optics, notion of a generalized measurement, state collapse

after quantum measurement, recovery of states passed through a noisy quantum

system, the Knill-Laflamme theorem Stinespring’s representation of noisy

quantum systems, Information, relative entropy, mutual information and Renyi

entropy of quantum systems. Transmission of information over quantum system.

The relevance of all this to the wave mechanics of Schrodinger.

32. Controlling the quantum em field produced by electrons and positrons by using a classical em field-An application of Dirac’s relativistic wave equation.

33. Calculating the path of a light ray in a static gravitational field

34. A study of thermal emission by black holes via Hawking radiation, quantum

mechanics of fields in the vicinity of a black hole and the interaction of electrons, positrons, photons and gravitons with an external noisy bath with

application to the design of very large size quantum gates.

35. Wave digital filter design.

36. Large deviation principle in wave-motion.

37. Some more problems in Schrodinger-wave mechanics and Heisenberg matrix

mechanics with relevance to quantum information theory

38. Questions in optimization techniques.

39. Quantum antennas via the Schrodinger wave equation.

40. Linear algebra for quantum information theory.

41. Transmission lines and waveguides–Questions.

42. Some more matrix inequalities related to quantum information theory.

43. Fresnel and Fraunhoffer diffraction.

44. Surface tension and wave propagation.

45. Klein-Gordon equation in the Schwarzschild space-time with a radial time

independent electromagnetic field and its application to computing the Hawking

temperature at which massless/massive particles are emitted from a black hole

46. Quantum Belavkin filtering versus classical Kushner-Kallianpur filtering–

A comparison.

47. Remark on quantum Belavkin filtering for estimating the state of a quantum vibrating string.

48. Elementary problems in robotics based on damped simple harmonic motion.

49. Approximate solution to the Dirac equation in curved space-time.

50. Some applications of quantum gate design using physical systems.

51. Convergence of perturbation series for nonlinear differential equations.

52. Poiseulle’s law and generalized Poiseulle’s law for flow through a pipe.

53. Measurement of refractive index.

54. Modes of a vibrating string with applications to particle physics.

55. Hidden Markov Models for estimating the amplitude, frequency and phase of a sinusoidal signal making transitions.

56. The energy-momentum tensor of the Dirac field in a background curved space-time metric

57. Remark on Noether’s theorem on conserved currents

58. Energy-momentum tensor using the tetrad formalism.

59. Analysis of gravitational waves produced by a finite system of point

particles–A perturbation theoretic approach.

60. Heat equation and its solution in Rn, relationship between heat and

wave equations, nonlinear heat equations arising as the scaling limit of the

simple exclusion process

61. Study of wave motion of the boundary of single cellular micro-organsims

by giving them external stimulus and observing the wave like motion of their

boundary walls as well as wave-like fluctuations of the velocity field of the cytoplasmic

fluid within them

62. Snell’s laws of reflection and refraction on surfaces separating two uniform

media.

63. Spinor form of some equations of mathematical physics:Roger Penrose’s

theory

64. Prisms, mirrors and lenses, the general theory

65. A brief summary of the book

This is a book about all the mathematical aspects of wave motion including the fundamental equations governing sound waves in a pipe, waves in the sea, electromagnetic waves with applications to geometrical optics and diffraction theory, gravitational waves as predicted by Einstein’s general theory of relativity, quantum mechanical waves, namely the dynamics of the wave function arising in Schrodinger’s wave equation for atomic systems both without and with noise. It also includes the general theory of lenses and prisms. A separate section of the book includes some general aspects of probability and random processes both from classical and quantum probabilistic angle. This section has been written keeping in mind general aspects of filtering theory wherein one proposes to estimate wave motion dynamics from noisy measurements. Electromagnetic waves inside confined walls like waveguides and cavity resonators are also dealt with in some detail. The book will be useful to undergraduate and postgraduate students of physics, applied mathematics and electronics and communication engineering. The sections dealing with quantum probability and quantum filtering will be useful to the advanced researcher in applied mathematics as well as to researchers in quantum optics. Each chapter of the book has four sections, one summary, two technical discussion, three points to remember and four exercises. This makes the material easy to understand for even an undergraduate student of physics.

1.The Definition of a propagating wave in one, two and three dimensions.

2.Standing waves in one, two and three dimensions.

3.The polarization of a wave.

4.The wave equation in one, two and three dimensions.

One dimensional waves in a vibrating string.

Two dimensional waves in a vibrating membrane.

Three dimensional waves in optics.

5.The polarization of a wave.

6.Basics of fluid dynamics.

7.Waves in a fluid–derivation from first principles

8.Longitudinal sound/pressure waves in a tube.

9.The difference between transverse and longitudinal waves in terms of wave

polarization.

10. Maxwell’s equations and the wave equation for the electric and magnetic

fields in free space.

11. Solution to Maxwell’s equations in terms of retarded potentials satisfying

the wave equation with source.

12. The principle of superposition.

13. Diffraction and interference of waves.

14. Green’s function for wave equation with sources–Fraunhoffer and Fresnel’s

diffraction.

15.The basic Eikonal equation of geometric optics.

16.Describing the trajectory of light in a medium having spatially varying

refractive index.

17. Propagation of light in anisotropic, inhomogeneous and time varying

medium

18. The Schrodinger wave equation in quantum mechanics

19. The effect of noise on the Schrodinger wave equation–Open systems, ie,

coupling of the system to the bath environment.

20. Wave equation with random non-uniform refractive index.

21. The relationship between the wave equation and the Helmholtz equation

for waves of given frequency

22. Waves in a confined region.

23. Schrodinger’s wave equation for mixed states in the position kernel

domain.

24. Gravitational waves in flat space-time and curved space-time background.

25. Quantum gravity, the canonical ADM formalism-Schrodinger’s equation

for the wave function of the space-time metric.

26. Plasma waves.

27. Evans-Hudson diffusion as a quantum mechanical generalization of the

wave equation with noise.

28. Waves in an expanding universe–Newtonian theory of small fluctuations

and general relativistic theory of small fluctuations.

29. EM waves in a curved space-time geometry with inhomogeneous permittivitypermeability

tensor.

30. Quantum Optics. Here, the photon field is a quantum electromagneticfield expressible as a superposition of annihilation and creation operators of the photon field with the coefficients of the linear combination being positions of

time and space.

31. Quantum optics, notion of a generalized measurement, state collapse

after quantum measurement, recovery of states passed through a noisy quantum

system, the Knill-Laflamme theorem Stinespring’s representation of noisy

quantum systems, Information, relative entropy, mutual information and Renyi

entropy of quantum systems. Transmission of information over quantum system.

The relevance of all this to the wave mechanics of Schrodinger.

32. Controlling the quantum em field produced by electrons and positrons by using a classical em field-An application of Dirac’s relativistic wave equation.

33. Calculating the path of a light ray in a static gravitational field

34. A study of thermal emission by black holes via Hawking radiation, quantum

mechanics of fields in the vicinity of a black hole and the interaction of electrons, positrons, photons and gravitons with an external noisy bath with

application to the design of very large size quantum gates.

35. Wave digital filter design.

36. Large deviation principle in wave-motion.

37. Some more problems in Schrodinger-wave mechanics and Heisenberg matrix

mechanics with relevance to quantum information theory

38. Questions in optimization techniques.

39. Quantum antennas via the Schrodinger wave equation.

40. Linear algebra for quantum information theory.

41. Transmission lines and waveguides–Questions.

42. Some more matrix inequalities related to quantum information theory.

43. Fresnel and Fraunhoffer diffraction.

44. Surface tension and wave propagation.

45. Klein-Gordon equation in the Schwarzschild space-time with a radial time

independent electromagnetic field and its application to computing the Hawking

temperature at which massless/massive particles are emitted from a black hole

46. Quantum Belavkin filtering versus classical Kushner-Kallianpur filtering–

A comparison.

47. Remark on quantum Belavkin filtering for estimating the state of a quantum vibrating string.

48. Elementary problems in robotics based on damped simple harmonic motion.

49. Approximate solution to the Dirac equation in curved space-time.

50. Some applications of quantum gate design using physical systems.

51. Convergence of perturbation series for nonlinear differential equations.

52. Poiseulle’s law and generalized Poiseulle’s law for flow through a pipe.

53. Measurement of refractive index.

54. Modes of a vibrating string with applications to particle physics.

55. Hidden Markov Models for estimating the amplitude, frequency and phase of a sinusoidal signal making transitions.

56. The energy-momentum tensor of the Dirac field in a background curved space-time metric

57. Remark on Noether’s theorem on conserved currents

58. Energy-momentum tensor using the tetrad formalism.

59. Analysis of gravitational waves produced by a finite system of point

particles–A perturbation theoretic approach.

60. Heat equation and its solution in Rn, relationship between heat and

wave equations, nonlinear heat equations arising as the scaling limit of the

simple exclusion process

61. Study of wave motion of the boundary of single cellular micro-organsims

by giving them external stimulus and observing the wave like motion of their

boundary walls as well as wave-like fluctuations of the velocity field of the cytoplasmic

fluid within them

62. Snell’s laws of reflection and refraction on surfaces separating two uniform

media.

63. Spinor form of some equations of mathematical physics:Roger Penrose’s

theory

64. Prisms, mirrors and lenses, the general theory

65. A brief summary of the book