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Schrodinger |Adam Adams | Experiential Facts of Life MIT | Lecture 5
MIT Physics Lecture 5 Schrodinger | Quantum Physics 1 | Adam Adams
Professor Zwiebach provides a mathematical overview of operators in this lecture. He next goes over some basic quantum mechanics postulates related to measurement and observables. The beginnings of the Schrödinger equation are the subject of the lecture's final section. Teacher: Allan Adams
Citation Youtube MIT Opencourseware
The Schrödinger equation can be thought of as the quantum equivalent of Newton's second law in classical physics. Newton's second law predicts mathematically
the course a given physical system will take over time given a set of specified initial conditions. The wave function's evolution over time, or the quantum-mechanical
characterisation of a single physical system, is provided by the Schrödinger equation. Schrödinger derived the equation using Louis de Broglie's postulate,
which states that every matter has a corresponding matter wave. The atom's bound states were predicted by the equation and agreed with experimental findings.
There are several methods for researching and predicting quantum mechanical systems than the Schrödinger equation. Werner Heisenberg created matrix mechanics,
and Richard Feynman primarily developed the path integral formulation of quantum mechanics. The application of the Schrödinger equation is sometimes referred to
as "wave mechanics" when comparing different methods. The relativistic variant of the Schrödinger equation is a wave equation known as the Klein-Gordon equation.
Due to the presence
of a first derivative in time and a second derivative in space, which implies that space and time are not on an equal footing, the Schrödinger equation is nonrelativistic.
Special relativity and quantum mechanics
Special relativity and quantum mechanics were combined by Paul Dirac into a single formulation that, in the non-relativistic limit, reduces to the Schrödinger equation. There is just one derivative in space and time, and that is the Dirac equation. Even though the Klein-Gordon equation was a relativistic wave equation, its second-derivative PDE resulted in a probability density issue. A negative probability density would be physically impossible. Dirac corrected this by first creating Dirac matrices and then taking the Klein-Gordon operator's so-called square-root. The Dirac equation describes spin-1/2 particles in a modern setting, whereas the Klein-Gordon equation describes spin-less particles. The Schrödinger equation is usually introduced in introductory physics
The Schrödinger equation's form is dependent on the physical context. The time-dependent Schrödinger equation, which describes a system changing over time,
is the most general version.
The Schrödinger equation is usually introduced in introductory physics or chemistry classes in a form that is understandable with only a rudimentary understanding
of calculus principles and notation, namely derivatives with regard to space and time. The position-space Schrödinger
equation for a single nonrelativistic particle in one dimension is a particular case of the Schrödinger equation that admits a statement in those terms:
Citation Schrodinger Equation Wikipedia
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