Wave function

• A wave function provides information about the probabilities of various possible states the system might be in. It depends on the coordinates of the particles in the system (for example, position or momentum). It calculates the probability of finding the system in a particular state.
• Wave functions are used to determine the probability of various outcomes in quantum experiments.
• A wave function, in the context of quantum mechanics, must encapsulate a wealth of information about a quantum system, including its possible states, probabilities, and how it evolves over time:
  • Position and Momentum: The wave function must provide information about the possible positions and momenta of particles within the system. This information is crucial for predicting the outcomes of measurements.
  • Superposition: It should be able to represent the idea that a quantum system can exist in a superposition of multiple possible states. This means that the system can simultaneously occupy different states with certain probabilities until observed.
  • Probability Amplitudes: The wave function encodes probability amplitudes, which are complex numbers that determine the likelihood of finding the system in a particular state upon measurement.
  • Time Evolution: It should be able to evolve over time, allowing for the prediction of how the system’s state will change over the course of time.
  • Observable Properties: The wave function must account for the possible values of observable properties (such as energy, angular momentum, etc.) and their corresponding probabilities.
  • Normalization: It must satisfy the condition of normalization, meaning that the total probability of finding the system in any possible state must equal 1.
  • Boundary Conditions: For specific physical systems, the wave function must satisfy appropriate boundary conditions that reflect the constraints imposed on the system (e.g., within a finite box or in a specific potential field).
  • Interference and Entanglement: It should be capable of describing interference effects between different states and, in the case of multiple particles, account for entanglement, where the states of particles become correlated.
  • Wave Function Collapse: When a measurement is made, the wave function must be capable of undergoing a transition from a superposition of states to a single, definite state, in accordance with the process of wave function collapse.
  • Completeness and Orthogonality: In certain mathematical formulations of quantum mechanics, wave functions must form a complete and orthogonal set to be used as a basis for representing quantum states.

Wave Function Collapse

Wave function collapse is a phenomenon in quantum mechanics where the act of making a measurement on a quantum system causes it to transition from a superposition of multiple possible states to a single, definite state.

• Prior to measurement, a quantum system can exist in a superposition of states, meaning it simultaneously occupies multiple possible states with different probabilities – these are described by the wave. However, when a measurement is made, the wave function collapses, and the system assumes one of the possible states with certainty.
• Wave function collapse illustrates the profound influence that observation has on the behaviour of quantum systems.
• In the context of quantum mechanics, “observation” refers to the act of making a measurement or carrying out an experiment to gain information about a quantum system. When we observe a quantum system, we are attempting to determine one of its properties, such as position, momentum, energy, etc.
• The interpretation of wave function collapse is a subject of ongoing debate among physicists, with various interpretations positing different explanations for the phenomenon.