Non-relativistic quantum mechanics

This book develops and simplifies the concept of quantum mechanics based on the postulates of quantum mechanics. The text discusses the technique of disentangling the exponential of a sum of operators, closed under the operation of commutation, as the product of exponentials to simplify calculations of harmonic oscillator and angular momentum. Based on its singularity structure, the Schrödinger equation for various continuous potentials is solved in terms of the hypergeometric or the confluent hypergeometric functions. The forms of the potentials for which the one-dimensional Schrödinger equation is exactly solvable are derived in detail. The problem of identifying the states of two-level systems which have no classical analogy is addressed by going beyond Bell-like inequalities and separability. The measures of quantumness of mutual information in two two-level systems is also covered in detail. Offers a new approach to learning quantum mechanics based on the history of quantum mechanics and its postulates Covers advance topics such as the foundations of quantum mechanics, quantum information theory and nano-science in detail Discusses density operator in general, and that of one- and two-level systems One-dimensional potentials for which the Schrödinger equation is exactly solvable are identified and explained comprehensively A general theory of one-dimensional partially and completely periodic potentials for the study of nano and bulk solids is developed