Wave Function as superposition of eigenstates

In summary, a wave function is a mathematical description of the quantum state of a physical system, representing the probability amplitude of the system's possible quantum states. Superposition is the principle that allows a system to exist in multiple quantum states simultaneously, and in the context of wave functions, it means that the wave function can be a combination of different eigenstates. Eigenstates are the possible states of a system that can exist independently without changing over time, and in the context of wave functions, they represent the possible quantum states that a system can be in. When a wave function is a superposition of eigenstates, it is a combination of different eigenstates with different probabilities, providing a more accurate description of the quantum state of a system. This concept
  • #1
mavyn
7
0
Hi!

How can I write the wave function of a particle in an infinite box (in the state n) as a superposition of the eigenstates of the momentum operator?

the wave function is:

PHIn(x,t) = sqrt(2/a) * Sin(n * PI/a * x) * exp(-i En/h * t)

Thanks for your help!
 
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  • #2
well what are the basic solutions to py =ky for the momentum operator P? (BTW what are the solution of y"=ky?)

Can you express, say, the Sine function in term of these functions? (Try the expressing Sine in terms of exponentials via Euler's Identity.)
 

Related to Wave Function as superposition of eigenstates

1. What is a wave function?

A wave function, also known as a quantum state, is a mathematical description of the quantum state of a physical system. It describes the probability amplitude of the system's possible quantum states.

2. What is superposition in the context of wave functions?

Superposition is the principle that states that a physical system can exist in multiple quantum states at the same time. In the context of wave functions, it means that the wave function can be a combination of different eigenstates.

3. What are eigenstates?

Eigenstates, also known as stationary states, are the possible states of a system that can exist independently without changing over time. In the context of wave functions, they represent the possible quantum states that a system can be in.

4. What does it mean for a wave function to be a superposition of eigenstates?

A wave function being a superposition of eigenstates means that it is a combination of different eigenstates with different probabilities. This allows for a more accurate description of the quantum state of a system, as it takes into account the possibility of the system being in multiple states simultaneously.

5. How does the concept of superposition affect our understanding of quantum mechanics?

The concept of superposition is a fundamental principle of quantum mechanics and has significant implications for our understanding of the behavior of particles at the quantum level. It allows for the description of phenomena such as interference and entanglement, which cannot be explained by classical physics. It also plays a crucial role in the development of quantum technologies such as quantum computing and cryptography.

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