Week 1 Flashcards
What is the primary purpose of a quantum wavefunction?
To describe the quantum state of a particle or system.
True or False: The wavefunction can be directly observed in experiments.
False
In quantum mechanics, what symbol is commonly used to represent the wavefunction?
Ψ (Psi)
Fill in the blank: The wavefunction is a function of ______ and ______.
position and time
What does the square of the wavefunction’s absolute value represent?
The probability density of finding a particle in a given state.
Which equation describes how wavefunctions evolve over time?
The Schrödinger equation.
Multiple Choice: What is the form of the time-dependent Schrödinger equation?
iħ ∂Ψ/∂t = HΨ
What is ‘ħ’ in the context of quantum mechanics?
Reduced Planck’s constant.
True or False: The wavefunction can be a complex function.
True
What does a wavefunction collapse refer to?
The transition from a superposition of states to a single eigenstate upon measurement.
What are eigenstates?
States of a quantum system that correspond to a definite value of an observable.
Fill in the blank: The normalization condition for a wavefunction states that the integral of |Ψ|² over all space must equal ______.
1
Multiple Choice: Which of the following is NOT an allowable solution to the Schrödinger equation?
A wavefunction that is not square-integrable.
What is the physical interpretation of a wavefunction with a high probability density?
It indicates a greater likelihood of finding the particle in that region of space.
True or False: Wavefunctions can be added together to form new wavefunctions.
True
What is the principle of superposition in quantum mechanics?
A system can exist in multiple states simultaneously until measured.
Fill in the blank: The wavefunction must be ______ and ______ to be physically realizable.
normalizable and continuous
What is the role of the Hamiltonian operator in quantum mechanics?
It represents the total energy of the system and acts on the wavefunction.
Multiple Choice: Which of the following is a property of wavefunctions?
They must be continuous and differentiable.
What does the term ‘quantization’ refer to in quantum mechanics?
The concept that certain properties, like energy, can only take discrete values.
True or False: The wavefunction uniquely determines the behavior of a quantum system.
True
What is the significance of boundary conditions in solving wavefunction equations?
They ensure that the wavefunction is physically acceptable in a given domain.
Fill in the blank: The time-independent Schrödinger equation is used to solve for stationary ______.
states
Multiple Choice: Which of the following describes the wave-particle duality?
Particles exhibit both wave-like and particle-like properties.
