Wavefunction Equations Flashcards
(26 cards)
What is a wavefunction?
A wavefunction is a mathematical description of the quantum state of a system.
True or False: The wavefunction contains all the information about a quantum system.
True
Fill in the blank: The wavefunction is usually denoted by the symbol ____.
psi (Ψ)
What does the square of the wavefunction’s absolute value represent?
The probability density of finding a particle in a given state.
What is the significance of the normalization condition for a wavefunction?
The normalization condition ensures that the total probability of finding a particle in all space is equal to 1.
Which equation describes the time evolution of a wavefunction?
The Schrödinger equation.
What is the time-dependent Schrödinger equation?
iħ ∂Ψ/∂t = HΨ, where H is the Hamiltonian operator.
What does the Hamiltonian operator represent in quantum mechanics?
The total energy of the system.
What is a stationary state in quantum mechanics?
A stationary state is a quantum state with all observables independent of time.
True or False: A wavefunction can be complex-valued.
True
What is the principle of superposition in quantum mechanics?
The principle that a quantum system can exist in multiple states simultaneously until measured.
What type of wavefunction corresponds to a particle in a one-dimensional box?
Standing wavefunctions.
What is the relationship between wavefunctions and operators in quantum mechanics?
Operators act on wavefunctions to extract physical observables.
Fill in the blank: The wavefunction must be ____ to be physically acceptable.
normalizable
What is the Born rule?
The Born rule states that the probability of finding a particle in a given region of space is given by the square of the absolute value of the wavefunction.
What does a wavefunction collapse refer to?
The process by which a wavefunction’s probabilistic nature resolves into a definite state upon measurement.
In quantum mechanics, what does it mean for two wavefunctions to be orthogonal?
Two wavefunctions are orthogonal if their inner product is zero, indicating they represent distinct states.
What is the significance of the uncertainty principle in relation to wavefunctions?
The uncertainty principle implies limitations on the precision of simultaneously measuring certain pairs of observables.
What is a wave packet?
A wave packet is a superposition of wavefunctions that describes a localized particle.
True or False: Wavefunctions can be used to describe both particles and waves.
True
What does it mean for a wavefunction to be continuous?
A continuous wavefunction has no abrupt changes, ensuring physical plausibility.
What is the significance of boundary conditions in wavefunction solutions?
Boundary conditions determine the allowed states and energy levels of a quantum system.
What is the role of the wavefunction in quantum tunneling?
The wavefunction allows for the probability of a particle to penetrate a potential barrier.
Fill in the blank: The wavefunction’s phase can affect ____ but not the probability density.
interference
