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I am trying to read into quantum mechanics and am reading a lot of rules that do not cite evidence and while it is probably just the books I am reading, I was wondering if anyone could post some links to experiments that verify some of this.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

 

[paranormal]

As a fellow scientist, I completely understand your confusion and desire for evidence-based information in your study of quantum mechanics. It is important to note that quantum mechanics is a highly complex and abstract field, and not all concepts can be easily visualized or explained through everyday experiences. However, there are many experiments that have been conducted and verified by numerous scientists that support the principles and rules of quantum mechanics.

One example is the double-slit experiment, which demonstrates the wave-like behavior of particles such as electrons. In this experiment, a beam of electrons is fired at a barrier with two slits, and the resulting pattern on a screen behind the barrier shows an interference pattern, similar to what would be expected of waves. This experiment has been repeated numerous times and provides evidence for the wave-particle duality of particles in quantum mechanics.

Another experiment that supports the idea of "disorderly curves" when measuring the coordinates of electrons is the Heisenberg Uncertainty Principle. This principle states that it is impossible to know both the exact position and momentum of a particle at the same time. This has been tested and verified through a variety of experiments, including the Compton scattering experiment, which showed that the more precisely the position of an electron is measured, the less precisely its momentum can be known.

I would recommend looking into these and other experiments, as well as reading from a variety of sources, to gain a better understanding of the evidence behind the principles of quantum mechanics. It is also important to keep in mind that quantum mechanics is a constantly evolving field, and new experiments and evidence are continually being discovered. So while some concepts may seem abstract and difficult to grasp, they are supported by numerous experiments and continue to be validated by ongoing research. I wish you the best of luck in your studies.