Quantum Mechanics Fundamentals

Normalization ensures that the probability of finding a particle somewhere in space is 1, while orthogonality guarantees that the probability of finding a particle in a particular state is independent of other states.

The probability current density represents the flow of probability, and the equation of continuity ensures probability conservation, relating to the probability density and its time derivative.

A linear Hermitian operator represents a measurable quantity, such as position, momentum, angular momentum, or energy.

<p>The Ehrenfest theorem states that the expectation value of an operator obeys the classical equation of motion, describing the time evolution of the expectation value of a dynamical variable.</p> Signup and view all the answers

<p>Zero-point energy is the energy remaining in the ground state of a system, and in the simple harmonic oscillator, it represents the energy associated with the fluctuations in the oscillator's motion.</p> Signup and view all the answers

<p>The tunnel effect is a quantum phenomenon where a particle can pass through a potential barrier, and it is related to the transmission coefficient, which describes the probability of transmission.</p> Signup and view all the answers