Help understanding measured coordinates of an electron, etc. Examples?

[Jetik]

I am trying to read into quantum mechanics and am reading a lot of rules that do not cite evidence and while it is probably just the books I am reading, I was wondering if anyone could post some links to experiments that verify some of this.

First of all, this book "Quantum Mechanics - Non-relativistic Theory" by one Landau states that when the coordinates of electrons are measured at definite time intervals, the more precise the measurement then the more disorderly the curve will become. I am not following why the measurements would be on a curve to start with and I can not find experimental examples of their deviation when measured in Google.

I know that it is not your job to educate me and thank anyone who offers help.

 

[hilbert2]

First of all, this book "Quantum Mechanics - Non-relativistic Theory" by one Landau states that when the coordinates of electrons are measured at definite time intervals, the more precise the measurement then the more disorderly the curve will become.

To measure the position of the electron, you have to scatter some other particle off it. If you want the measurement to be precise, the scattered particle needs to have short De Broglie wavelength (high energy). The scattering event changes the electrons momentum, and this disruption of the electron's state of motion is larger if the scattered particle has high energy. This explains why a more precise measurement disturbs the electrons measured trajectory more significantly.

I am not following why the measurements would be on a curve to start with

Any possible set of points belongs on some kind of curve.

 

[Jetik]

That makes perfect sense, thank you. The book was giving me the impression that the measurements were chaotic as the electrons were not moving through space normally but rather jumping around.

When you say that any set up points belongs on a curve, is that because they are mapping 3d coordinates onto a 2d grid?

 

[hilbert2]

That makes perfect sense, thank you. The book was giving me the impression that the measurements were chaotic as the electrons were not moving through space normally but rather jumping around.

In theory of quantum mechanics, an electron does not have a definite position and does not move "normally" in the classical sense. The state of the electron is described by a wave function that gives probability amplitudes for its likelyhood to be in different positions. The evolution of the wave function is determined by the time dependent Schrodinger equation, if you know the wave function at some initial moment t₀ you can calculate what it is at a later moment t₀ + Δt . Only immediately after a position measurement is the electron temporarily localized to a definite point in space.

As I described when talking about measuring a particle's position by a scattering experiment, you can't observe an electrons position or any other dynamical variable without disturbing the electron. The more accurately you try to follow the behavior of the electron, the more you disturb it. The electron's undisturbed behavior is not something that is observable. In the philosophy of science, it is generally accepted that only those things that can be observed, can be said to "exist" (see e.g. Bishop Berkeley, "Esse est percipi!"). Therefore in quantum mechanics, we completely give up trying to talk about a particles "real trajectory".

When you say that any set up points belongs on a curve, is that because they are mapping 3d coordinates onto a 2d grid?

For any given set of points in a space of any dimensionality, we can mathematically construct a curve that goes through all the points.