baba-schrodinger-equation Flashcards
What equation governs the wave function of a quantum-mechanical system?
The Schrödinger equation
The Schrödinger equation is a linear partial differential equation that describes the time evolution of the wavefunction of a quantum mechanical system.
What does the wave function contain?
Statistical information about the quantum system
The Copenhagen interpretation views the wave function as containing statistical information about the quantum system.
How did Schrödinger derive his equation?
By treating particles as waves and extending de Broglie’s ideas
Schrödinger derived his equation by treating particles as matter waves, as proposed by de Broglie, and extending these ideas into a proper 3D wave equation.
What are some key properties of the Schrödinger equation?
- Linearity
- Unitarity
- Allows separation of variables
The Schrödinger equation is linear, meaning superpositions of solutions are also solutions. It evolves quantum states unitarily. It also allows separation of variables for simplification.
What are some example systems the Schrödinger equation can be solved for exactly?
- Particle in a box
- Harmonic oscillator
- Hydrogen atom
The Schrödinger equation has been solved exactly for systems like the particle in a box, harmonic oscillator, and hydrogen atom.
How did Max Born interpret the wave function?
As a probability amplitude
Born successfully interpreted the wave function as a probability amplitude, whose modulus squared gives a probability density.
What are the relativistic wave equations extending the Schrödinger equation?
- Klein-Gordon equation
- Dirac equation
Relativistic wave equations like the Klein-Gordon and Dirac equations extend the Schrödinger equation to relativistic situations.
How is the wave function interpreted in _______ interpretations?
many-worlds
In many-worlds interpretations, the wave function describes multiple parallel universes all existing simultaneously.
What mathematical tool is useful for mixed states in quantum mechanics?
Density matrix
Density matrices are useful for describing mixed states in quantum mechanics.
