Schrödinger equation | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-24

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation


00:02:45 1 Equation
00:02:53 1.1 Time-dependent equation
00:07:02 1.2 Time-independent equation
00:08:37 2 Derivation
00:11:31 3 Implications
00:11:54 3.1 Total, kinetic, and potential energy
00:12:27 3.2 Quantization
00:13:21 3.3 Measurement and uncertainty
00:14:28 3.4 Quantum tunneling
00:15:08 3.5 Particles as waves
00:18:07 3.6 Many-worlds interpretation
00:18:41 4 Interpretation of the wave function
00:19:46 5 Historical background and development
00:26:49 6 The wave equation for particles
00:28:46 6.1 Consistency with energy conservation
00:31:57 6.2 Linearity
00:34:49 6.3 Consistency with the de Broglie relations
00:35:08 6.4 Wave and particle motion
00:35:19 7 Nonrelativistic quantum mechanics
00:44:19 7.1 Time-independent
00:50:29 7.2 One-dimensional examples
00:52:00 7.2.1 Free particle
00:52:50 7.2.2 Constant potential
00:55:55 7.2.3 Harmonic oscillator
01:03:37 7.3 Three-dimensional examples
01:05:47 7.3.1 Hydrogen atom
01:05:57 7.3.2 Two-electron atoms or ions
01:06:05 7.4 Time-dependent
01:08:33 8 Solution methods
01:08:42 9 Properties
01:11:04 9.1 Linearity
01:19:10 9.2 Momentum space Schrödinger equation
01:25:02 9.3 Real energy eigenstates
01:25:17 9.4 Space and time derivatives
01:27:06 9.5 Local conservation of probability
01:29:05 9.6 Positive energy
01:39:28 9.7 Analytic continuation to diffusion
01:39:37 9.8 Regularity
01:39:58 10 Relativistic quantum mechanics
01:43:45 11 Quantum field theory
01:49:44 12 First order form
01:51:40 13 See also
01:55:26 14 Notes
01:57:32 15 References
02:01:15 16 External links
02:03:01 Regularity
02:04:27 Relativistic quantum mechanics
02:09:30 Quantum field theory
02:09:58 First order form
02:12:03 See also



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SUMMARY
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In quantum mechanics, the Schrödinger equation is a mathematical equation that describes the changes over time of a physical system in which quantum effects, such as wave–particle duality, are significant. These systems are referred to as quantum (mechanical) systems. The equation is considered a central result in the study of quantum systems,  and its derivation was a significant landmark in the development of the theory of quantum mechanics. It was named after Erwin Schrödinger, who derived the equation in 1925, and published it in 1926, forming the basis for his work that resulted in him being awarded the Nobel Prize in Physics in 1933.In classical mechanics, Newton's second law (F = ma) is used to make a mathematical prediction as to what path a given physical system will take over time following a set of known initial conditions.  Solving this equation gives the position, and the momentum of the physical system as a function of the external force F on the system. Those two parameters are sufficient to describe its state at each time instant.  In quantum mechanics, the analogue of Newton's law is Schrödinger's equation for a quantum system (usually atoms, molecules, and subatomic particles whether free, bound, or localized). The equation is mathematically described as a linear partial differential equation, which describes the time-evolution of the system's wave function (also called a "state function").The concept of a wave function is a fundamental postulate of quantum mechanics, that defines the state of the system at each spatial position, and time.  Using these postulates, Schrödinger's equation can be derived from the fact that the time-evolution operator must be unitary, and must therefore be generated by the exponential of a self-adjoint operator, which is the quantum Hamiltonian. This derivation is explained below. 
In the Copenhagen interpretation of quantum mechanics, the wave function is the most complete description that can be given of a physical system. Solutions to Schrödinger's equation describe not only molecular, atomic, and subatom ...