There is no gap between Maxwell’s equations and quantum mechanics. However, it is required to understand the relationship between quantum mechanics, Maxwell’s equations and applied remote sensing especially microwave remote sensing. This chapter attempts to deliver a wide understanding of Maxwell’s equations from the point of view of quantum mechanics. In fact, recent advanced computing tools are reconstructed based on quantum computing. In the next chapters, quantum algorithms will be implemented for automatic detection of the oil spill in radar images.
There is no gap between Maxwell’s equations and quantum mechanics. However, it is required to understand the relationship between quantum mechanics, Maxwell’s equations and applied remote sensing especially microwave remote sensing. This chapter attempts to deliver a wide understanding of Maxwell’s equations from the point of view of quantum mechanics. In fact, recent advanced computing tools are reconstructed based on quantum computing. In the next chapters, quantum algorithms will be implemented for automatic detection of the oil spill in radar images.
This chapter delivers a novel explanation quantized theory behind remote sensing. In this perspective, the quantized of Maxwell's Equations are addressed. This chapter also addressed a new definition of remote sensing. Needless to say, remote sensing is the quantum information amassed from any object on the ground or space owing to the reflection or backscattering of photons, which is a function of the quantum mechanical properties of every object's atoms. In this understanding, different object atoms would interact with photons, i.e., absorption and emission as a function of their different wavelengths and frequencies under circumstances of the uncertain principle of Heisbenger. This new definition of remote sensing delivers a new era of quantum image processing to obtain accurate information about the universe. The uncertainty of conventional remote sensing image processing could be issued owing to conventional computing techniques which are based on the classical computer system i.e. bit. It is also understanding quantum remote sensing technology based on Marghany's [ 33 ] definition, many mysteries in atmospheric turbulence can be tackled. In this regard, the next chapter will deliver answers to the mysteries of the High-Frequency Active Auroral Research Program (HAARP) impacts on the ionospheric layer.
In chapter 2, following the Maxwell description, we discuss vector potential, the continuity equation, and energy and momentum corresponding to optical fields. Based on the Maxwell depiction, quantization of electromagnetic fields is obtained. Quantized electromagnetic fields, such as Fock states, coherent states, squeezed states, and Schrödinger cat states, provide a general understanding of the quantum nature of the field. Thereby, we build the necessary foundation-level knowledge required to understand electromagnetic fields in the quantum domain.
The classical or semiclassical theory presented in Chapter 2 gives a satisfactory account of light-matter interactions in some cases. However, a detailed understanding of different processes requires a quantum mechanical theory of radiation. The quantum theory of light, like classical theory, is also based on Maxwell's equations. However, in quantum theory the electric field F and the magnetic field H are treated as operators. This chapter develops the correspondence between the two and outlines the method for converting field vectors F and H into quantum mechanical operators. Topics discussed include wave equation in a rectangular cavity, quantization of the electric field, time-dependent perturbation theory, interaction of an electron with the magnetic field, and second-order perturbation theory. Exercises are provided at the end of the chapter.
An accessible introduction to advanced quantum theory, this graduate-level textbook focuses on its practical applications rather than mathematical technicalities. It treats real-life examples, from topics ranging from quantum transport to nanotechnology, to equip students with a toolbox of theoretical techniques. Beginning with second quantization, the authors illustrate its use with different condensed matter physics examples. They then explain how to quantize classical fields, with a focus on the electromagnetic field, taking students from Maxwell's equations to photons, coherent states and absorption and emission of photons. Following this is a unique master-level presentation on dissipative quantum mechanics, before the textbook concludes with a short introduction to relativistic quantum mechanics, covering the Dirac equation and a relativistic second quantization formalism. The textbook includes 70 end-of-chapter problems. Solutions to some problems are given at the end of the chapter and full solutions to all problems are available for instructors at www.cambridge.org/9780521761505.
Despite its successes, quantum mechanics (QM) has remained mysterious to all who have encountered it. Starting with Bohr and progressing into the present, the departure from intuitive, physical reality has widened. The connection between QM and reality is more than just a “philosophical” issue. It reveals that QM is not a correct or complete theory of the physical world and that inescapable internal inconsistencies and incongruities arise when attempts are made to treat it as physical as opposed to a purely mathematical “tool.” Some of these issues are discussed in a review by F. Laloe [Am. J. Phys. 69, 655 (2001)]. In an attempt to provide some physical insight into atomic problems and starting with the same essential physics as Bohr of e moving in the Coulombic field of the proton and the wave equation as modified by Schrodinger, a classical approach is explored that yields a remarkably accurate model and provides insight into physics on the atomic level. The proverbial view, deeply seated in the wave-particle duality notion, that there is no large-scale physical counterpart to the nature of the electron may not be correct. Physical laws and intuition may be restored when dealing with the wave equation and quantummechanical problems. Specifically, a theory of classical quantum mechanics (CQM) is derived from first principles that successfully applies physical laws on all scales. Rather than using the postulated Schrodinger boundary condition “Ψ → 0 as r → ∞,” which leads to a purely mathematical model of the electron, the constraint is based on experimental observation. Using Maxwell’s equations, the classical wave equation is solved with the constraint that the bound (n = 1)state electron cannot radiate energy. By further application of Maxwell’s equations to electromagnetic and gravitational fields at particle production, the Schwarzschild metric is derived from the classical wave equation, which modifies general relativity to include conservation of spacetime in addition to momentum and matter/energy. The result gives a natural relationship among Maxwell’s equations, special relativity, and general relativity. CQM holds over a scale of spacetime of 85 orders of magnitude — it correctly predicts the nature of the universe from the scale of the quarks to that of the cosmos. A review is given by G. Landvogt [Internat. J. Hydrogen Energy 28, 1155 (2003)].
Maxwell’s equations, formulated in 1865, preceded quantum mechanics by six decades. When the logical direction is reversed, however, the electromagnetic field structure can be interpreted as the form required for a quantum theory of charged matter once three standard ingredients are imposed: local gauge invariance, conserved electric current, and a dynamical electromagnetic field. Quantum mechanics supplies the charged-particle state, probability amplitudes, quantum currents, and—through the Dirac equation—a relativistically consistent description of electron charge and spin. Gauge symmetry then organizes the electromagnetic interaction, while current conservation constrains the admissible source structure. The homogeneous Maxwell identities follow naturally from expressing the field through a four-potential, whereas the sourced Maxwell equations require an additional electromagnetic field action or equivalent dynamical assumption. The resulting framework clarifies both the strength and the limit of a “Maxwell from quantum mechanics” program: quantum theory and gauge structure strongly constrain electromagnetism, but Maxwell field dynamics are not obtained from the electron wave equation alone.