Handling coherent states by undergraduates students may be a hard task, as they have to deal with Glauber's series $e^{-\frac {|\alpha|^2} {2}}\sum\limits_{n=0}^\infty\frac {\alpha^n} {\sqrt{n!}}\phi_n(x)$. We show here that the task can be greatly simplified by introduction of a novel compact formula for Glauber coherent states employed in [ Int. J. Mod. Phys. B {\bf 31} (2017) 175051]. This expression is obtained by solving the basic differential equation associated to coherent states $a|\alpha>=\alpha|\alpha>$.
Handling coherent states by undergraduates students may be a hard task, as they have to deal with Glauber's series e−2∣α∣2n=0∑∞n!αnϕn(x). We show here that the task can be greatly simplified by introduction of a novel compact formula for Glauber coherent states employed in [ Int. J. Mod. Phys. B {\bf 31} (2017) 175051]. This expression is obtained by solving the basic differential equation associated to coherent states a∣α>=α∣α>.
Written for use in teaching and for self-study, this book provides a comprehensive and pedagogical introduction to groups, algebras, geometry, and topology. It assimilates modern applications of these concepts, assuming only an advanced undergraduate preparation in physics. It provides a balanced view of group theory, Lie algebras, and topological concepts, while emphasizing a broad range of modern applications such as Lorentz and Poincaré invariance, coherent states, quantum phase transitions, the quantum Hall effect, topological matter, and Chern numbers, among many others. An example based approach is adopted from the outset, and the book includes worked examples and informational boxes to illustrate and expand on key concepts. 344 homework problems are included, with full solutions available to instructors, and a subset of 172 of these problems have full solutions available to students.
Based on years of teaching experience, this book provides a clearly structured and accessible introduction to the fundamental principles of quantum mechanics, tailored for undergraduate students. The text builds a strong conceptual and mathematical foundation while promoting intuitive understanding and critical thinking. Students progress from basic concepts such as wave mechanics to more advanced topics within matrix mechanics. Complex concepts are presented in a diligent and understandable way, achieving a balance between conceptual insight and mathematical rigor without oversimplifying the subject. Thoroughly class-tested, this book is designed to support both classroom instruction and independent study. It will serve as a great tool for undergraduates studying introductory and intermediate quantum mechanics, as well as modern physics and quantum systems for engineers.
Quantum Science and Technology (QST) has rapidly emerged as a transformative domain, driving advances in computing, sensing, and communication. The global expansion of quantum research and education programs reflects the recognition of quantum technologies as central to twenty-first-century scientific and technological progress. Sustaining this trajectory requires cultivating a workforce with strong conceptual and technical foundations in quantum science. Yet, significant pedagogical challenges persist, particularly in designing curricula that balance theoretical rigor with accessibility for students with basic understanding of ordinary differential equations. This study seeks to address a critical gap in undergraduate quantum mechanics instruction by introducing a tractable framework for solving the Schrödinger equation with noncentral potentials. Such potentials—including ring-shaped interactions—are indispensable for modelling molecular structures, anisotropic systems, and ultracold collision phenomena. Despite their importance, their mathematical complexity has historically hindered integration into standard coursework, leaving students underprepared for contemporary quantum applications. We develop a differential-equation-based approach that explicitly solves the orbital component of the Schrödinger equation under a noncentral potential. The resulting normalized wavefunctions are expressed in terms of Jacobi polynomials. The framework is designed to be mathematically rigorous yet pedagogically accessible, enabling undergraduate students to engage with noncentral potentials without requiring advanced mathematical tools beyond the standard curriculum. The solutions obtained demonstrate clear dependence on both potential parameters and quantum numbers, while maintaining consistency with established results in the literature. This validates the framework’s accuracy and suitability for instructional use. By simplifying the mathematical treatment without sacrificing rigor, the approach provides students with meaningful exposure to complex quantum systems. This work offers a pathway for incorporating noncentral potentials into undergraduate quantum mechanics instruction. By broadening the conceptual toolkit available to students, it supports the development of a versatile quantum-ready workforce and advances the integration of contemporary quantum applications into mainstream education.
q-Deformed coherent states associated with the sequence xnq,α=(1+αqn−1)[n]q
Photonics deals with the applications of light in science and technology including a vast number of different topics from engineering to telecommunications, to medicine, computing, metrology, and on and on. The book covers different topics related to the properties of the coherent interaction of light with matter in the frame of classical electrodynamics introducing the basic concepts in this field to undergraduate students and young researchers approaching this field. The contents include a revision of the fundamental properties of light and of the classical theory of light emission and intro-duces the basic equations describing the propagation of light beams and light pulses, including light propagation in uniaxial crystals and diffraction. A list of solved problems is included at the end of each chapter and the bibliography at the end covers both a basic and a more specialized literature for those students likely to go more deeply into the fascinating ideas of this field.
Written for use in teaching and for self-study, this book provides a comprehensive and pedagogical introduction to groups, algebras, geometry, and topology. It assimilates modern applications of these concepts, assuming only an advanced undergraduate preparation in physics. It provides a balanced view of group theory, Lie algebras, and topological concepts, while emphasizing a broad range of modern applications such as Lorentz and Poincaré invariance, coherent states, quantum phase transitions, the quantum Hall effect, topological matter, and Chern numbers, among many others. An example based approach is adopted from the outset, and the book includes worked examples and informational boxes to illustrate and expand on key concepts. 344 homework problems are included, with full solutions available to instructors, and a subset of 172 of these problems have full solutions available to students.