SphericalCs

 I think of it as home ground (le plancher des vaches), referred to in the

St-Andrew's as the Azimuthal Plane. Here denoted by the Greek letter phi;

one measures the angle form the x-axis to the y. The polar angle (theta) is measured

from the z-axis.

                                                                      

The German Wikipedia page on spherical coordinates sees this as the 'usual' 

convention.

The French Wikipedia page introduces an also - Polar - with a reversal of Greek letters and

an angle measure from ground toward the z-axis.

Anglophone Wikipedia presents the German 'usual' as the physics convention: those finicky

physicists reverse the letters!! Below, widget using the Anglophone norm...

Spherical coordinates - Math Insight

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I am re-running my Hello World code on the IBM  Brisbane platform, but I am in a queue with

a few hours to wait!! 👩‍💻

https://youtu.be/qJCh53SdS6s?si=p_vAr1FEn5kWNqFt

From Gemini Ai:

We can't directly measure the wave function itself, which gives us information about the probability of finding a quantum particle at a specific location and time. However, there are two main approaches to  determining the wave function values of a quantum system:

1. **Solving the Schrödinger Equation:**

The Schrödinger equation is a fundamental equation in quantum mechanics that relates the wave function of a system to its total energy. By solving this equation for a specific system, considering its potential energy and other properties, we can obtain the theoretical wave function.

2. **Experimental Measurements:**

While we cannot measure the wave function directly, we can perform experiments to gather data about the probabilities of finding the particle in certain states. This data can then be used to infer the wave function itself. For instance, in a double-slit experiment, the interference pattern on the screen provides information about the probability distribution of the particle, which can be linked back to the wave function.

It's important to remember that the wave function is a mathematical construct and not a physical property like position or momentum. It provides us with probabilities, not certainties, about the quantum system. 

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The job from IBM quantum in Brisbane came back. Below:

                                                               

More along the lines of what was expected. Although, it shows very little

entanglement at all. This is urprising; the code normalizes the distance

between qubits 1 and 2 as the reference relationship...