Stationary State

Definition

A stationary state refers to a quantum state of a system that does not change in time, characterized by a wave function that is a solution to the time-independent Schrödinger equation. In this state, the probabilities of finding a particle in various locations remain constant over time, providing a stable configuration of the system’s energy and spatial distribution.

5 Must Know Facts For Your Next Test

1. In a stationary state, the probability density associated with the wave function remains constant over time, which means that measurements made on the system yield consistent results.
2. Stationary states correspond to energy eigenstates; each state has a specific energy value and remains unchanged as time progresses.
3. The wave functions of stationary states are typically sinusoidal and can be represented as standing waves, reflecting their stable nature.
4. When observing a quantum system in a stationary state, the expectation values of physical observables do not change with time, providing predictable measurements.
5. Transitioning from one stationary state to another involves an energy change and corresponds to absorbing or emitting energy, typically in the form of photons.

Review Questions

• How does a stationary state differ from other quantum states in terms of time dependence and measurement outcomes?
  • A stationary state is unique because it does not change over time; its wave function remains constant, leading to stable measurement outcomes. In contrast, non-stationary states evolve with time, meaning their probability distributions can shift and vary during observation. This stability allows for predictable properties in stationary states, making them critical for understanding energy levels in quantum systems.
• Discuss how stationary states relate to energy eigenstates and their significance in quantum mechanics.
  • Stationary states are directly tied to energy eigenstates, as each stationary state corresponds to a specific energy level within a quantum system. These energy eigenstates are solutions to the time-independent Schrödinger equation, indicating that they maintain consistent properties when measured. Understanding these states is essential for analyzing how systems behave under different energy conditions and predicting their reactions to external influences.
• Evaluate the implications of transitioning between stationary states in terms of energy conservation and photon emission or absorption.
  • Transitioning between stationary states indicates that a quantum system is either absorbing or emitting energy, which is often manifested as photon interaction. This process must adhere to the conservation of energy; thus, the energy difference between the two states must equal the energy of the emitted or absorbed photon. Analyzing these transitions helps us understand spectral lines in atomic physics and provides insight into fundamental processes like electron excitations and relaxations within atoms.

Related terms

Wave Function:

A mathematical function that describes the quantum state of a particle or system, containing all the information about the system's properties and behavior.

Time-Independent Schrödinger Equation:

An equation that describes how the wave function of a quantum system evolves in space without considering time, used to find stationary states.

Energy Eigenstate: A specific type of stationary state where the wave function corresponds to a definite energy level of the system, leading to predictable behavior.