The Mathematics of Quantum Coin-Flipping

A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes,...

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.

Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when an outcome cannot be divided into simpler parts.
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.

Bias refers to any tendency that prevents a question from being considered unprejudiced. In research, bias occurs when one outcome or answer is selected or encouraged over others in sampling or testing. Bias can occur during any research phase, including study design, data collection, analysis, and publication.
In statistics, a sampling bias is created when a sample is collected from a population, and some members of the population are not as likely to be chosen as others (remember, each member...