Undergrad Is there any physical significance to Wave Amplitude?

[reis1212]

I am studying Quantum physics and I'm having some problems to understand what is the Wave Amplitude since I can't find a physical significance to it. Does anyone ever heard something that come close to a physical significance?

 

[Nugatory]

Do you mean the amplitude of the wave function $\psi(x,t)$ which is the solution of Schrodinger's equation?

Also, what book are you studying QM from? You'll get more and more helpful answers if we know what you're working with.

 

[lomidrevo]

Isn't this a subject of QM interpretations?

 

[PeroK]

I am studying Quantum physics and I'm having some problems to understand what is the Wave Amplitude since I can't find a physical significance to it. Does anyone ever heard something that come close to a physical significance?

A key concept in QM is that of the (complex) probability amplitude, which governs how probabilities work and represents a fundamental difference from classical physics.

 

[reis1212]

Yes, the solution of Schrodinger's equation. English isn't my mother language so i didn't know how to refeer to it. I am using Tipler but I didn't find a analogy. Does it even have a physical significance?

 

[atyy]

The wave function is used to calculate probability of the various measurement outcomes. For example, if position is measured, the probability of observing various positions is $P(x) = |\psi(x)|^{2}$. The formula is different if one measures another quantity such as energy or momentum, but always involves the wave function.

The Schroedinger equation predicts how the wave function changes with time between measurements. At the point of measurement, the Schroedinger equation does not apply, and the wave function undergoes a discontinuous change called "collapse" or "state reduction" that depends on the measurement result.

 

[vanhees71]

To be more precise $P(x)=|\psi(x)|^2$ is the probability distribution for the particle's position. For continuous variables you have always probability distributions rather than probabilities. The meaning is that the probability to find the particle in an "infinitesimally small interval" $\mathrm{d}(x)$ around the position $x$ is given by $\mathrm{d} x P(x)=\mathrm{d} x |\psi(x)|^2$.

Of course the probability for the particle being somewhere is $1$, i.e., all this holds if the wave function is properly normalized, i.e.,
$$\int_{\mathbb{R}} \mathrm{d} x P(x) = \int_{\mathbb{R}} \mathrm{d} x |\psi(x)|^2=1.$$
This is the standard interpretation of the physical meaning of the wave function, and it's good advice to abstain from reading about all kinds of alternative "interpretations" and other philosophical issues until you have a good understanding of quantum mechanics within its standard interpretation. The best interpretation to learn QT is not to bother about these overly confusing (and in many cased also indeed confused) metaphysical ideas but stick to the "shutup and calculation interpretation", which is best expressed in the Feynman Lectures vol. III, which I highly recommend to read in parallel with Tipler. It's even legally free to read online:

https://www.feynmanlectures.caltech.edu/