What is the wavelike behavior of an electron in superposition?

[Kiki]

Does a superposed state of an electron exist over a larger amount of space than the state of an electron as a particle?

 

[houlahound]

You would have to define the boundary conditions, energy etc of the system to answer.

 

[DrClaude]

Does a superposed state of an electron exist over a larger amount of space than the state of an electron as a particle?

I don't understand what you mean. Can you rephrase the question?

 

[Kiki]

I am comparing the particle version of an electron to the electron in a superposition of possible states. The particle is assumed to be concentrated in one region and not in a superposition, and the particle has experienced decoherence. On the other hand, the electron described by superposition is mathematically composed of a linear combination of states, and I am wondering if those states are thought to exist over a wider range of space than in the space that the particle exists.

 

[vanhees71]

The point is that you can't say a vector is "in superposition". A vector is a vector. It can be decomposed into superpositions of any other vectors. A particularly important superposition is to express the vector as a linear combination with respect to a basis, in QT most conveniently in terms of a orthonormal basis. You have to specify which basis you mean to say which "superposition" you mean.

 

[PeroK]

I am comparing the particle version of an electron to the electron in a superposition of possible states. The particle is assumed to be concentrated in one region and not in a superposition, and the particle has experienced decoherence. On the other hand, the electron described by superposition is mathematically composed of a linear combination of states, and I am wondering if those states are thought to exist over a wider range of space than in the space that the particle exists.

I think you are fundamentally misunderstanding the QM nature of an electron. Do you have in mind the state of a free electron after a measurement of its position?

 

[Kiki]

I think you are fundamentally misunderstanding the QM nature of an electron. Do you have in mind the state of a free electron after a measurement of its position?

I have in mind the state of a free electron as it travels through space. Such an electron would be in superposition with itself, right?

 

[PeroK]

I have in mind the state of a free electron as it travels through space. Such an electron would be in superposition with itself, right?

That statement makes no sense to me. How much QM do you know? Are you learning it yourself?

 

[Kiki]

That statement makes no sense to me. How much QM do you know? Are you learning it yourself?

I am currently learning QM on my own, yes.

Maybe that statement would make more sense in the context of the double slit experiment for electrons. If one electron travels through a double slit diffraction grating, one of the conclusions from that experiment is that the electron interferes with itself when the electron is not measured.

 

[PeroK]

I am currently learning QM on my own, yes.

Maybe that statement would make more sense in the context of the double slit experiment for electrons. If one electron travels through a double slit diffraction grating, one of the conclusions from that experiment is that the electron interferes with itself when the electron is not measured.

Are we talking about a free electron or the double-slit experiment?

One last question: do you have a textbook? If not, what are you using to learn QM?

 

[Kiki]

Are we talking about a free electron or the double-slit experiment?

One last question: do you have a textbook? If not, what are you using to learn QM?

Double-slit experiment. Sorry for the confusion.

I have David Griffith's Introduction to Quantum Mechanics.

 

[PeroK]

Double-slit experiment. Sorry for the confusion.

I have David Griffith's Introduction to Quantum Mechanics.

What's your question about the double-slit experiment?

Does a superposed state of an electron exist over a larger amount of space than the state of an electron as a particle?

This makes no sense to me and suggests you haven't understood the concept of a wave function or the supporting mathematics. For example:

An electron is a particle and is fully described by its wave function, which is a function of time and position and represents the state of the particle.

How far have you got with Griffiths?

 

[Kiki]

I have read the first three chapters of Griffiths. I have watched some online lectures from universities as well.

If I remember correctly, decoherence is equivalent to wave function collapse. This decoherence, which is a consequence of measurement, causes a particle to be observed.

In the context of the double slit experiment, before measurement at a phosphorescent screen, the particle is mathematically described by a wave function that is a linear combination of states. One conclusion from the double slit experiment is that the electron must behave like a wave in order for the diffraction pattern to appear at a phosphorescent screen. By definition of a wave, this wave has to take up more space than the particle version of an electron that only travels through one slit, right?

I would also like to know how the wave behavior of the electron is linked to the wave function of the electron -- is the wave function of the electron the same as the wave behavior that must occur in order for a diffraction pattern to appear? If so, I think that would imply the wave function of an electron exists across more space than the wave function for the particle version of an electron.

 

[PeroK]

I have read the first three chapters of Griffiths. I have watched some online lectures from universities as well.

If I remember correctly, decoherence is equivalent to wave function collapse. This decoherence, which is a consequence of measurement, causes a particle to be observed.

In the context of the double slit experiment, before measurement at a phosphorescent screen, the particle is mathematically described by a wave function that is a linear combination of states. One conclusion from the double slit experiment is that the electron must behave like a wave in order for the diffraction pattern to appear at a phosphorescent screen. By definition of a wave, this wave has to take up more space than the particle version of an electron that only travels through one slit.

I would like to know how the wave behavior of the electron is linked to the wave function of the electron -- is the wave function of the electron the same as the wave behavior that must occur in order for a diffraction pattern to appear? If so, I think that would imply the wave function of an electron exists across more space than the wave function for the particle version of an electron.

What you have written, IMO, shows the influence of pop-science videos! None of that could come from Griffiths, not least because:

a) He doesn't use the term decoherence.

b) He doesn't cover the double-slit experiement.

c) He never talks about a particle having "wave-like" behaviour or the wave-particle duality.

One answer:

The wave function of a particle is not the same as a particle having "wavelike" behaviour. That is a fundamental misunderstanding on your part.

And one suggestion:

I would stick to Griffiths and learn QM from him (that's the real deal) and forget the pop-science videos you've been watching.

 

[Kiki]

Alright, thank you for pointing that out! I'll need to be more careful with what I accept as facts.

 

[Kiki]

I still have a question though, what is the "wavelike" behavior of the electron?
Here is a useful reference: http://iopscience.iop.org/article/10.1088/1367-2630/15/3/033018/pdf

 

[PeroK]

I still have a question though, what is the "wavelike" behavior of the electron?
Here is a useful reference: http://iopscience.iop.org/article/10.1088/1367-2630/15/3/033018/pdf

As I said, Griffiths does not explain or use the term "wave-particle" duality. What it doesn't mean is that an electron is "sometimes a wave and sometimes a particle".

Try this: