It is not uncommon to come across the phrase Hilbert space in any book of quantum mechanics, with the author mentioning Hilbert space as if the exact mathematical description of the Hilbert space is a nuance that can be relegated to a side study. For example, we have Susskind and Friedman, in their book Quantum… Read More »
Quantum mechanics demands that every quantum system corresponds to a separable Hilbert space. The separability condition requires that the Hilbert space possesses a countable set of basis vectors. A collection of objects or a set is called countable if it has a finite number of members or elements; or, in the case of infinite number… Read More »
Introduction We, physicists, work with our operators very differently from mathematicians. We are unencumbered by rigor and our mathematics proceeds with the motivation to forge ahead to gain insight as quickly as possible. Only later when our results are meaningful that we bother to step back and ask ourselves if our steps in reaching our… Read More »
Introduction A system is an object or a collection of objects whose properties are subject to observation and measurement. The state of a given system is the minimum collection of information that completely describes the system. For a classical particle, its state is specified by giving its position and momentum at any given time. The… Read More »