Quantum Mechanics for Beginners

Wikipedia

 

Quantum mechanics is the body of scientific principles that explains the behaviour of matter and its interactions with energy on the scale of atoms andsubatomic particles, and how these phenomena could be related to everyday life (see: Schrodinger's cat).

Classical physics explains matter and energy at the macroscopic level—on a scale familiar to human experience—including the behaviour of astronomical bodies. It remains the key to measurement for much of modern science and technology. On the other hand, toward the end of the 19th century, scientists discovered phenomena in both the large (macro) and the small (micro) worlds that classical physics could not explain. Coming to terms with these limitations led to the development of quantum mechanics, a major revolution in physics. This article describes how physicists discovered the limitations of classical physics and developed the main concepts of the quantum theory that replaced it in the early decades of the 20th century.^{[note 1]} These concepts are described in roughly the order they were first discovered; for a more complete history of the subject, see History of quantum mechanics.^[1]

Some aspects of quantum mechanics can seem counter-intuitive or even paradoxical, because they describe behaviour quite different than that seen at larger length scales, where classical physics is an excellent approximation. In the words of Richard Feynman, quantum mechanics deals with "nature as She is – absurd."^[2]

Many types of energy, such as photons (discrete units of light), behave in some respects like particles and in other respects like waves. Radiators of photons (such as neon lights) have emission spectra that are discontinuous, in that only certain frequencies of light are present. Quantum mechanics predicts the energies, the colours, and the spectral intensities of all forms of electromagnetic radiation.

Quantum mechanics ordains that the more closely one pins down one measurement (such as the position of a particle), the less precise another measurement pertaining to the same particle (such as its momentum) must become. This is called the uncertainty principle, also known as the Heisenberg principle after the person who first proposed it.

Even more disconcerting, pairs of particles can be created as "entangled twins." As is described in more detail in the article on Quantum entanglement, entangled particles seem to exhibit what Einstein called "spooky action at a distance," matches between states that classical physics would insist must be random even when distance and the speed of light ensure that no physical causation could account for these correlations.^[3]

Jeanette Cain

The importance and excitement of quantum mechanics is often lost through sheer intimidation of those two words. One does not need a doctorate degree to understand the fundamental concepts of quantum mechanics. If you view it as a source of entertainment with amazing abilities, you may discover you know more than you ever dreamed possible. One of the most important steps to understanding any subject is to understand the definitions of the words involved. It is a wise person that keeps a dictionary nearby.

Quantum mechanics is the study of matter and radiation at an atomic level. During the 20th century, certain experiments produced results unexplainable by the classical physics of Newton and Galileo, for example. Classical physics means the physics of everyday life. Quantum mechanics importance is shown through the wave-particle dualities, tunneling, spinning of a particle and the Heisenberg uncertainty principle. If these words intimidate you, pull out the dictionary and you'll discover you know more than originally thought!

In physics, quantum is energy, also known as a unit. It is the smallest imaginable amount of energy, which is capable of acting independently. Independent means capable of action without help from another. If you act independently, you are saying that you use your own ideas and you have no need to follow the rest of the crowd. Quantum and humans seem to have similar philosophies.

Mechanics is the branch dealing with the action of forces on bodies and motion, including the areas of kinetics, statics and kinematics. Force is the power and strength to control, or influence. Once again, humans and quantum have similarities.

When obvious flaws began to show in previous physic theories, relativity and quantum mechanics were developed to cope with these problems. At first, relativity was used to describe the physics of very fast, massive objects. Quantum mechanics began in the 1920's for the purpose of describing the physics of little tiny objects. Most of the advanced science technologies of the present would not have come into existence without the use of quantum mechanics.

The scientists and Nobel Prize winners associated with quantum mechanics continue to face uncertainties and doubts on the actions and mechanics, but that does not make it impossible to be known or experienced. Many problems facing this area of study is with differences of interpretation. However, it was a difference of interpretations that brought its existence into light.

There are many who may have interpretations and logical thoughts on quantum mechanics, but are afraid they have neither the intellect nor a degree-bearing name to justify giving it their time and study. Everyone encounters quantum mechanics on a daily basis. Are you the next light bearer of new thoughts for the next century?

Dummies

Quantum Physics and the Hamiltonian

One of the central problems of quantum mechanics is to calculate the energy levels of a system. The energy operator, called the Hamiltonian, abbreviated H, gives you the total energy. Finding the energy levels of a system breaks down to finding the eigenvalues of the problem

The eigenvalues can be found by solving the equation:

Quantum Physics and the Heisenberg Uncertainty Principle

In quantum physics, you encounter the Heisenberg uncertainty principle, which says that the better you know the position of a particle, the less you know the momentum, and vice versa. In the xdirection, for example, that looks like this:

where Dx is the measurement uncertainty in the particle’s x position, Dp_x is its measurement uncertainty in its momentum in the x direction, and

This relation holds for all three dimensions:

Quantum Physics and the Schrödinger Equation

When a quantum mechanical state can be described by a wave function,

then this is a solution of the Schrödinger equation, which is written in terms of the potential

and energy

like so:

The Schrödinger equation work in three dimensions as well:

Spin Operators and Commutation in Quantum Physics

Don’t think quantum physics is devoid of anything but dry science. The fact is that it’s full of relationships, they’re just commutation relationships — which are pretty dry science after all. In any case, among the angular momentum operators L_x, L_y, and L_z, are these commutation relations:

All the orbital angular momentum operators, such as L_x, L_y, and L_z, have analogous spin operators: S_x, S_y, and S_z. And the commutation relations work the same way for spin:

Quantum Physics and the Compton Effect

In quantum physics, you may deal with the Compton effect of X-ray and gamma ray qualities in matter. To calculate these effects, use the following formula, which assumes that the light is represented by a photon with energy E = hu and that its momentum is p = E/c:

 

 

Bioshock Infinite Timeline