# Systems with more than 1 wave function

• ghost313
In summary, the equation ψ(x) = ∑n anψn(x) expresses the principle of superposition in quantum mechanics, where quantum states form a vector space. It does not necessarily mean that particles are interacting with each other. Quantum Field Theory describes all particles as excitations in the same underlying field. The concept of a quantum state is interpretation dependent and can be further discussed in a separate thread.
ghost313
Hello,I am new to quantum mechanics.I just want to clear this equation:

ψ(x) = ∑n anψn(x)

What does this actually mean?Is this equation telling us that the system is moving as a wave?
Or,as I think,for example let's suppouse we have 2 electrons in a system,and the wave function becomes this ψ(x),does that mean that electrons interact one with the other?

That's not a physical statement but a mathematical one and only means that we're using some base functions to expand the wavefunction, like expanding a 3D vector in terms of $\hat x, \hat y$ and $\hat z$.

ghost313
No, actually multiparticle systems use the concept of tensor product of uniparticle spaces. So the product, not the sum appears in the formula of a general state.

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ghost313
I red somewhere that there are quantum fields which imply that one wave function(1 electron) can intercept on another wave functions (1 or more electrons),and so reverse...eaven when r → ∞ r(distance) so their Potential Energy(V) V → 0.
What does that mean then?
Thank you btw for answearing.

ghost313 said:
I red somewhere that there are quantum fields

In Quantum Field Theory you don't have one particle. All the electrons in the universe are described by excitations in the same underlying field.

Regarding your original question your equation simply expresses the fact quantum states form a vector space - this is known as the principle of superposition.

Exactly what a quantum state is is a difficult issue being very interpretation dependant. If you want to pursue that best to start a new thread.

Thanks
Bill

vanhees71 and ghost313

## 1. What are systems with more than 1 wave function?

Systems with more than 1 wave function refer to physical systems that have multiple possible wave functions, each describing a different state of the system. These systems are typically studied in quantum mechanics and can include particles, atoms, and molecules.

## 2. How do these systems differ from systems with a single wave function?

Systems with more than 1 wave function are more complex than systems with a single wave function, as they can exist in multiple states simultaneously. This is known as superposition and is a fundamental principle of quantum mechanics.

## 3. What is the significance of systems with more than 1 wave function?

Systems with more than 1 wave function allow scientists to better understand the behavior of quantum systems and make predictions about their properties. They also play a crucial role in technologies such as quantum computing and cryptography.

## 4. How are these systems studied and analyzed?

Scientists use mathematical models and techniques, such as the Schrödinger equation, to study and analyze systems with more than 1 wave function. These models help to predict the probabilities of different states and behaviors of the system.

## 5. What are some real-world examples of systems with more than 1 wave function?

One example of a system with more than 1 wave function is the hydrogen atom, which has multiple possible energy states described by different wave functions. Other examples include the behavior of electrons in a crystal lattice, and the spin states of particles such as protons and neutrons in an atomic nucleus.

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