Definition of stationary state (for wave function quantum)

Thread starter AStaunton
Start date Mar 8, 2011
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Definition Function Quantum State Wave Wave function

In summary, a stationary state in quantum mechanics refers to a state of a quantum system where the probability density of finding the system in any particular state does not change with time. It is different from a non-stationary state, which is a state where the probability density changes with time. Stationary states are important in quantum mechanics because they represent the most stable and predictable states of a system, and they are related to the time-independent wave function of the system. A system can only be in one stationary state at a time, but it can transition between different stationary states over time.

Mar 8, 2011

AStaunton

Hi there

My textbook says the following is the time independant wave function for a stationary state:

[tex]\Psi(x,y,z,t)=\psi(x,y,z)e^{-iEt/\bar{h}}[/tex]

Just trying to get my definitions straight...is a stationary state the analogue of a standing wave?

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Mar 8, 2011

AStaunton

correction****

time DEpendant

What is a stationary state in quantum mechanics?

A stationary state in quantum mechanics refers to a state of a quantum system where the probability density of finding the system in any particular state does not change with time. This is also known as a time-independent state.

How is a stationary state different from a non-stationary state?

A non-stationary state, also known as a non-equilibrium state, is one where the probability density of finding the system in a particular state changes with time. This means that the system is not in a stable state and can undergo various changes over time. On the other hand, a stationary state is a stable state where the probability density remains constant over time.

What is the significance of stationary states in quantum mechanics?

Stationary states are important in quantum mechanics because they represent the most stable and predictable states of a system. They allow us to make predictions about the behavior of a system and can help us understand the properties and characteristics of a quantum system.

How are stationary states related to the wave function?

The wave function of a quantum system describes the probability amplitude of finding the system in a particular state. In a stationary state, the wave function is time-independent, meaning it does not change with time. This is because the energy of the system is constant in a stationary state, and the wave function is directly related to the energy of the system.

Can a system be in more than one stationary state at the same time?

No, a system can only be in one stationary state at a time. This is because a stationary state represents a specific energy level of the system, and a system can only have one energy level at a given time. However, a system can transition between different stationary states over time.