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SPIE eBooks

Modeling the Quantum World

Moamer Hasanovic

Published Aug 31, 2026• 0 citations
Publisher

Abstract

This chapter introduces core quantum mechanics concepts, focusing on Heisenberg's uncertainty principle and Schrödinger's equation, which describe quantum particles' wave–particle duality and probabilistic nature. The uncertainty principle and Schrödinger's equation are fundamental postulates validated by experiments, with the latter governing quantum behavior. The chapter explores wave functions, superposition, and entanglement, using light polarization to contrast classical and quantum interpretations, demonstrating that single photons exhibit probabilistic outcomes when interacting with polarizers. Additionally, it discusses polarizers and polarizing beam splitters, analyzing light propagation through these components using the law of Malus and comparing classical and quantum interpretations. The chapter concludes by highlighting the implications of these findings on photon polarization and measurement, providing a foundation for understanding quantum technologies.

DOI
10.1117/3.100443.ch5

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This chapter introduces core quantum mechanics concepts, focusing on Heisenberg's uncertainty principle and Schrödinger's equation, which describe quantum particles' wave–particle duality and probabilistic nature. The uncertainty principle and Schrödinger's equation are fundamental postulates validated by experiments, with the latter governing quantum behavior. The chapter explores wave functions, superposition, and entanglement, using light polarization to contrast classical and quantum interpretations, demonstrating that single photons exhibit probabilistic outcomes when interacting with polarizers. Additionally, it discusses polarizers and polarizing beam splitters, analyzing light propagation through these components using the law of Malus and comparing classical and quantum interpretations. The chapter concludes by highlighting the implications of these findings on photon polarization and measurement, providing a foundation for understanding quantum technologies.
This chapter introduces fundamental principles of quantum mechanics, focusing on wave–particle duality, superposition, entanglement, and quantum teleportation, systematically building from classical optics to quantum behavior using algebraic and trigonometric methods. Key arguments include the de Broglie hypothesis, validated by experiments such as Davisson and Germer, and quantum confinement, which results in discrete energy levels analogous to classical wave phenomena. The chapter explores quantum systems through historical experiments and theoretical frameworks, demonstrating wave properties and interference patterns, even for single particles, while introducing Pauli's exclusion principle and the Stern–Gerlach experiment. It concludes by highlighting the impact of observation on quantum systems, preparing students and professionals for further study in quantum technologies without requiring calculus.
Quantum Mechanics fundamentally redefines how we understand and predict physical phenomena at the microscopic level, diverging significantly from classical physics. This chapter introduces the core principles and mathematical tools that form the basis of quantum theory, emphasizing wave-particle duality, the quantum state concept, and the mechanism of wave function collapse. These concepts challenge traditional notions of determinism and locality, replacing them with probabilistic outcomes and non-local interactions. Understanding these principles is crucial for any advanced study in physics, chemistry, and related fields, as they lay the groundwork for exploring more complex quantum phenomena discussed in subsequent chapters.
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The previous chapter surveyed part of the rich variety of physical phenomena that can be understood using the ideas of quantum physics. Now that we are beginning the task of looking more deeply into the subject we shall find it useful to concentrate on examples that are comparatively simple to understand but which still illustrate the fundamental principles and highlight the basic conceptual problems. Some years ago most writers discussing such topics would probably have turned to the example of a ‘particle’ passing through a two-slit apparatus (as in Figure 1.2), whose wave properties are revealed in the interference pattern. Much of the discussion would have been in terms of wave–particle duality and the problems involved in position and momentum measurements, as in the discussion of the uncertainty principle in the last chapter. However, there are essentially an infinite number of places where the particle can be and an infinite number of possible values of its momentum, and this complicates the discussion considerably. We can illustrate all the points of principle we want to discuss by considering situations where a measurement has only a small number of possible outcomes. One such quantity relating to the physics of light beams and photons is known as polarisation . In the next section we discuss it in the context of the classical wave theory of light, and the rest of the chapter extends the concept to situations where the photon nature of light is important.
The previous chapter surveyed part of the rich variety of physical phenomena that can be understood using the ideas of quantum physics. Now that we are beginning the task of looking more deeply into the subject we shall find it useful to concentrate on examples that are comparatively simple to understand but which still illustrate the fundamental principles and highlight the basic conceptual problems. Some years ago most writers discussing such topics would probably have turned to the example of a ‘particle’ passing through a two-slit apparatus (as in Figure 1.2), whose wave properties are revealed in the interference pattern. Much of the discussion would have been in terms of wave–particle duality and the problems involved in position and momentum measurements, as in the discussion of the uncertainty principle in the last chapter. However, there are essentially an infinite number of places where the particle can be and an infinite number of possible values of its momentum, and this complicates the discussion considerably. We can illustrate all the points of principle we want to discuss by considering situations where a measurement has only a small number of possible outcomes. One such quantity relating to the physics of light beams and photons is known as polarisation . In the next section we discuss it in the context of the classical wave theory of light, and the rest of the chapter extends the concept to situations where the photon nature of light is important.