Position and Momentum Operators in Quantum Mechanics

Explore the mathematical foundations of quantum mechanics in this 26-minute video lecture on position and momentum operators. Delve into the complex mathematics underlying quantum theory, including linear algebra and differential equations. Learn about operators, their applications to wavefunctions, and the crucial roles of position and momentum operators in quantum mechanics. Discover how these concepts differ from classical physics and relate to key principles like the Heisenberg Uncertainty Principle and wave-particle duality. Gain insights into the de Broglie principle, properties of operators, and the commutator of position and momentum. While advanced mathematical knowledge is recommended, links to prerequisite math topics are provided for a comprehensive understanding of this fundamental aspect of modern physics.

Modern Physics Series
quantum mechanics requires advanced mathematics
quantum mechanics is math
relevant concepts in linear algebra and differential equations are covered in my mathematics series
together we will derive the equations of quantum mechanics
1 Visit my mathematics playlist, scroll down until the topics seem unfamiliar, and watch from that point through to the end of the list.
Classical Physics Series
Where is the particle located? Where will it be some specific time from now?
we can use this to predict the precise position and velocity of this particle at any time given the initial conditions
this does not work for quantum particles
Heisenberg Uncertainty Principle
Wave-Particle Duality
classical particles are macroscopic objects
the wavefunction (psi of x)
examples of operators
in quantum mechanics position and momentum are operators
de Broglie principle
Properties of Operators
commutator of position and momentum
PROFESSOR DAVE EXPLAINS