A question in one dimensional Schroedinger Equation.

In summary, the conversation discusses the potential field U(x) and its relationship to the solutions of the Schrödinger equation. It is stated that both ψ and ψ* can be solutions of the equation, but the complex conjugate is only a solution if the direction of time is reversed. It is also mentioned that including a reference to the source of the statement is helpful for future discussions.
  • #1
Karmerlo
14
0
I read something like this:

since U(x)(the potential field) is a real,ψ and ψ* can both be the solution of Schroedinger Equation.I cannot understand this. Anyone can give me an explanation.

Thanks.
 
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  • #2
I wrote something else here earlier, but I think what i said is wrong. A solution of the Schrödinger equation satisfies [tex]\psi(x,t)=e^{-iHt}\psi(x,0).[/tex] This implies [tex]\psi(x,t)^*=e^{iHt}\psi(x,0)^*.[/tex] So the complex conjugate is only a solution if we reverse the direction of time.

A tip for next time is that you include a reference to where you saw the statement, if possible with a link to the correct page at Google Books.
 
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  • #3
The time-independent Schrodinger equation is (-h2/2m) ψ(x) + U(x) ψ(x) = E ψ(x).
Take the complex conjugate of this equation, and since U and E are real, you get
(-h2/2m) ψ*(x) + U(x) ψ*(x) = E ψ*(x)
showing that ψ*(x) satisfies the same equation.
 

Related to A question in one dimensional Schroedinger Equation.

What is the one dimensional Schroedinger Equation?

The one dimensional Schroedinger Equation is a fundamental equation in quantum mechanics that describes the behavior of a quantum particle in one dimension. It is used to calculate the probability of finding a particle at a specific location in space and time.

What are the applications of the one dimensional Schroedinger Equation?

The one dimensional Schroedinger Equation has many applications in quantum mechanics, including predicting the behavior of atoms, molecules, and other quantum systems. It is also used in the development of new technologies such as quantum computing and nanotechnology.

How is the one dimensional Schroedinger Equation derived?

The one dimensional Schroedinger Equation is derived from the more general three-dimensional Schroedinger Equation, which describes the behavior of a quantum particle in three dimensions. It is derived using mathematical techniques such as partial differential equations and linear algebra.

What are the key components of the one dimensional Schroedinger Equation?

The one dimensional Schroedinger Equation has two key components: the Hamiltonian operator, which represents the total energy of the particle, and the wave function, which represents the probability of finding the particle at a specific location in space and time. These components are used to calculate the time evolution of a quantum system.

What are the implications of the one dimensional Schroedinger Equation for our understanding of the physical world?

The one dimensional Schroedinger Equation has profound implications for our understanding of the physical world. It challenges our classical understanding of particles and their behavior, and forces us to think about the probabilistic nature of reality at the quantum level. It also allows us to make accurate predictions about the behavior of complex systems, leading to advancements in technology and our understanding of the universe.

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