Quantum mechanics | Definition, Development, & Equations (2024)

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Written by

Gordon Leslie Squires Lecturer in Physics, University of Cambridge; Fellow of Trinity College, Cambridge. Author of Problems in Quantum Mechanics with Solutions and others.

Gordon Leslie Squires

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Key People:
Werner Heisenberg
John von Neumann
P.A.M. Dirac
Richard Feynman
Pascual Jordan
Related Topics:
quantum field theory
quantum
S-matrix
energy level
wave mechanics

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quantum mechanics, science dealing with the behaviour of matter and light on the atomic and subatomic scale. It attempts to describe and account for the properties of molecules and atoms and their constituents—electrons, protons, neutrons, and other more esoteric particles such as quarks and gluons. These properties include the interactions of the particles with one another and with electromagnetic radiation (i.e., light, X-rays, and gamma rays).

The behaviour of matter and radiation on the atomic scale often seems peculiar, and the consequences of quantum theory are accordingly difficult to understand and to believe. Its concepts frequently conflict with common-sense notions derived from observations of the everyday world. There is no reason, however, why the behaviour of the atomic world should conform to that of the familiar, large-scale world. It is important to realize that quantum mechanics is a branch of physics and that the business of physics is to describe and account for the way the world—on both the large and the small scale—actually is and not how one imagines it or would like it to be.

The study of quantum mechanics is rewarding for several reasons. First, it illustrates the essential methodology of physics. Second, it has been enormously successful in giving correct results in practically every situation to which it has been applied. There is, however, an intriguing paradox. In spite of the overwhelming practical success of quantum mechanics, the foundations of the subject contain unresolved problems—in particular, problems concerning the nature of measurement. An essential feature of quantum mechanics is that it is generally impossible, even in principle, to measure a system without disturbing it; the detailed nature of this disturbance and the exact point at which it occurs are obscure and controversial. Thus, quantum mechanics attracted some of the ablest scientists of the 20th century, and they erected what is perhaps the finest intellectual edifice of the period.

Historical basis of quantum theory

Basic considerations

At a fundamental level, both radiation and matter have characteristics of particles and waves. The gradual recognition by scientists that radiation has particle-like properties and that matter has wavelike properties provided the impetus for the development of quantum mechanics. Influenced by Newton, most physicists of the 18th century believed that light consisted of particles, which they called corpuscles. From about 1800, evidence began to accumulate for a wave theory of light. At about this time Thomas Young showed that, if monochromatic light passes through a pair of slits, the two emerging beams interfere, so that a fringe pattern of alternately bright and dark bands appears on a screen. The bands are readily explained by a wave theory of light. According to the theory, a bright band is produced when the crests (and troughs) of the waves from the two slits arrive together at the screen; a dark band is produced when the crest of one wave arrives at the same time as the trough of the other, and the effects of the two light beams cancel. Beginning in 1815, a series of experiments by Augustin-Jean Fresnel of France and others showed that, when a parallel beam of light passes through a single slit, the emerging beam is no longer parallel but starts to diverge; this phenomenon is known as diffraction. Given the wavelength of the light and the geometry of the apparatus (i.e., the separation and widths of the slits and the distance from the slits to the screen), one can use the wave theory to calculate the expected pattern in each case; the theory agrees precisely with the experimental data.

Early developments

Planck’s radiation law

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By the end of the 19th century, physicists almost universally accepted the wave theory of light. However, though the ideas of classical physics explain interference and diffraction phenomena relating to the propagation of light, they do not account for the absorption and emission of light. All bodies radiate electromagnetic energy as heat; in fact, a body emits radiation at all wavelengths. The energy radiated at different wavelengths is a maximum at a wavelength that depends on the temperature of the body; the hotter the body, the shorter the wavelength for maximum radiation. Attempts to calculate the energy distribution for the radiation from a blackbody using classical ideas were unsuccessful. (A blackbody is a hypothetical ideal body or surface that absorbs and reemits all radiant energy falling on it.) One formula, proposed by Wilhelm Wien of Germany, did not agree with observations at long wavelengths, and another, proposed by Lord Rayleigh (John William Strutt) of England, disagreed with those at short wavelengths.

In 1900 the German theoretical physicist Max Planck made a bold suggestion. He assumed that the radiation energy is emitted, not continuously, but rather in discrete packets called quanta. The energy E of the quantum is related to the frequency ν by E = hν. The quantity h, now known as Planck’s constant, is a universal constant with the approximate value of 6.62607 × 10−34 joule∙second. Planck showed that the calculated energy spectrum then agreed with observation over the entire wavelength range.

Quantum mechanics | Definition, Development, & Equations (2024)

FAQs

Quantum mechanics | Definition, Development, & Equations? ›

quantum mechanics, science dealing with the behaviour of matter and light on the atomic and subatomic scale. It attempts to describe and account for the properties of molecules and atoms and their constituents—electrons, protons, neutrons, and other more esoteric particles such as quarks and gluons.

What are the 4 types of quantum mechanics? ›

Answer: The four sectors of quantum mechanics are:
  • Quantization of physical properties.
  • Quantum entanglement.
  • Uncertainty principle.
  • Wave-particle duality.

What is the equation for quantum mechanics? ›

E=p22m+U(x,t), where p is the momentum, m is the mass, and U is the potential energy of the particle. The wave equation that goes with it turns out to be a key equation in quantum mechanics, called Schrӧdinger's time-dependent equation.

What are the 6 laws of quantum mechanics? ›

We propose six principles as the fundamental principles of quantum mechanics: principle of space and time, Galilean principle of relativity, Hamilton's principle, wave principle, probability principle, and principle of indestructibility and increatiblity of particles.

What is the hardest part of quantum mechanics? ›

The probabilistic nature of quantum mechanics thus stems from the act of measurement. This is one of the most difficult aspects of quantum systems to understand.

What is the nutshell of quantum mechanics? ›

Quantum mechanics is a mathematical description of how elementary particles move and interact in nature. It is based on the wave–particle dual description formulated by Bohr, Einstein, Heisenberg, Schrödinger, and others.

What is the most famous quantum physics equation? ›

The Schrödinger equation is a partial differential equation that governs the wave function of a quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics.

What is quantum mechanics in layman's terms? ›

Quantum mechanics is the field of physics that explains how extremely small objects simultaneously have the characteristics of both particles (tiny pieces of matter) and waves (a disturbance or variation that transfers energy). Physicists call this the “wave-particle duality.”

What is the basic rule of quantum mechanics? ›

THE TWO GOLDEN RULES OF QUANTUM MECHANICS

Rule 1: A particle can be in quantum superposition where it behaves as though it is both here and there. Rule 2: When measured, the particle will be found either here or there. Many phenomena predicted by quantum mechanics can be understood using these two simple rules.

What are the two golden rules of quantum? ›

Fermi's First Golden Rule is the result of applying second-order time-dependent perturbation theory to quantum scattering and resonances. Fermi's Second Golden Rule is the result of applying second-order time-dependent perturbation theory to absorption.

What is the first rule of quantum physics? ›

The first law of quantum physics states that the boundary between matter and energy is not always in a state of stability or finite; this means that everything is made of matter and energy. The relationship between matter and energy is exhibited at different anatomical levels.

What is a quantum in simple terms? ›

What is a quantum? A quantum (plural: quanta) is the smallest discrete unit of a phenomenon. For example, a quantum of light is a photon, and a quantum of electricity is an electron. Quantum comes from Latin, meaning "an amount" or "how much?" If something is quantifiable, then it can be measured.

What is a quantum physicist's salary? ›

Quantum Physicist Salary
Annual SalaryMonthly Pay
Top Earners$176,000$14,666
75th Percentile$112,000$9,333
Average$94,805$7,900
25th Percentile$59,000$4,916

Which is harder, general relativity or quantum mechanics? ›

General Relativity is more mathematically difficult than non-relativistic quantum mechanics (which is what most people mean when they say "quantum mechanics").

Can I learn quantum physics by myself? ›

That depends on how you learn. If you learn well by simply reading, you might go for a textbook or websites. If you search “Quantum Physics Textbook” online, you'll have no trouble finding one on Amazon.com or a similar site. You can even find PDF files of entire physics textbooks online for free.

What are the 4 pillars of quantum mechanics? ›

The main principles of Quantum Mechanics are Superposition, Wave-Particle Duality, the Uncertainty Principle, and Entanglement.

What are the 4 interpretations of quantum mechanics? ›

Objective-collapse theories
  • the Ghirardi–Rimini–Weber theory.
  • the continuous spontaneous localization model.
  • the Penrose interpretation.

What are the 3 main branches of quantum physics? ›

Quantum physics is the most recent course of study in physics. Here, scientists study quantum mechanics, quantum statistics, quantum electrodynamics, and quantum field theory. This branch deals primarily with objects at an atomic and subatomic level.

What are the 4 quantum variables? ›

Summary
Name and SymbolMeaning and Possible Values
Principal quantum number, nElectron shell, n ≥ 1
Azimuthal quantum number, lSubshells (s=0, p=1, etc.) , (n-1) ≥ l ≥ 0
Magnetic quantum number, mlTotal number and orientation of orbitals, l≥ml≥-l
Electron spin quantum number, msThe direction of electron spin, ms = ±½

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