classical mechanics

(noun)

All of the physical laws of nature that account for the behaviour of the normal world, but break down when dealing with the very small (see quantum mechanics) or the very fast or very heavy (see relativity).

Related Terms

  • al by-prod
  • special relativity
  • Lorentz factor

Examples of classical mechanics in the following topics:

  • The Bohr Model of the Atom

    • Bohr suggested that electrons in hydrogen could have certain classical motions only when restricted by a quantum rule.
    • The laws of classical mechanics predict that the electron should release electromagnetic radiation while orbiting a nucleus (according to Maxwell's equations, accelerating charge should emit electromagnetic radiation).
    • He suggested that electrons could only have certain classical motions:
    • In these orbits, the electron's acceleration does not result in radiation and energy loss as required by classical electrodynamics.
    • The significance of the Bohr model is that the laws of classical mechanics apply to the motion of the electron about the nucleus only when restricted by a quantum rule.
  • Overview of Temperature and Kinetic Theory

    • Classical mechanics defines the translational kinetic energy of a gas molecule as follows:
    • The distribution of the speeds (which determine the translational kinetic energies) of the particles in a classical ideal gas is called the Maxwell-Boltzmann distribution.
    • In kinetic theory, the temperature of a classical ideal gas is related to its average kinetic energy per degree of freedom Ek via the equation:
  • The Wave Function

    • A wave function is a probability amplitude in quantum mechanics that describes the quantum state of a particle and how it behaves.
    • In quantum mechanics, a wave function is a probability amplitude describing the quantum state of a particle and how it behaves.
    • The laws of quantum mechanics (the Schrödinger equation) describe how the wave function evolves over time.
    • This figure shows some trajectories of a harmonic oscillator (a ball attached to a spring) in classical mechanics (A-B) and quantum mechanics (C-H).
    • This "energy quantization" does not occur in classical physics, where the oscillator can have any energy.
  • Relativistic Kinetic Energy

    • In classical mechanics, the kinetic energy of an object depends on the mass of a body as well as its speed.
    • The classical kinetic energy of an object is related to its momentum by the equation:
    • At a low speed ($v << c$), the relativistic kinetic energy may be approximated well by the classical kinetic energy.
    • Thus, the total energy can be partitioned into the energy of the rest mass plus the traditional classical kinetic energy at low speeds.
    • Compare classical and relativistic kinetic energies for objects at speeds much less and approaching the speed of light
  • Lasers

    • Principles of laser operation are largely based on quantum mechanics.
    • (One exception would be free-electron lasers, whose operation can be explained solely by classical electrodynamics. ) When an electron is excited from a lower-energy to a higher-energy level, it will not stay that way forever.
    • This is the mechanism of fluorescence and thermal emission.
    • However, an external photon at a frequency associated with the atomic transition can affect the quantum mechanical state of the atom .
  • Simple Machines

    • They can be described as the simplest mechanisms that use mechanical advantage (or leverage) to multiply force.
    • Usually, the term "simple machine" is referring to one of the six classical simple machines, defined by Renaissance scientists.
    • For example, a bicycle is a mechanism made up of wheels, levers, and pulleys.
    • The ratio of the output force to the input force is the mechanical advantage of the machine.
    • For instance, the mechanical advantage of a lever is equal to the ratio of its lever arms.
  • Implications of Quantum Mechanics

    • Quantum mechanics has also strongly influenced string theory.
    • The application of quantum mechanics to chemistry is known as quantum chemistry.
    • Relativistic quantum mechanics can, in principle, mathematically describe most of chemistry.
    • A more distant goal is the development of quantum computers, which are expected to perform certain computational tasks exponentially faster than classical computers.
    • Explain importance of quantum mechanics for technology and other branches of science
  • Atomic Structure

    • So far we have used classical and semi-classical approaches to understand how radiation interacts with matter.
    • We have generally treat the electrons (the lightest charged particle so the biggest emitter) classically and the radiation either classically or as coming in quanta (i.e. semi-classically).
    • We also derived some important relationships between how atoms emit and absorb radiation, but to understand atomic processes in detail we will have to treat the electrons quantum mechanically.
    • In quantum mechanics we characterize the state of a particles (or group of particles) by the wavefunction ($\Psi$).
    • We can imagine the operator $H$ as a matrix that multiplies the state vector $\psi$, so this equation is an eigenvalue equation with $E$ as the eigenvalue and $\psi$ as an eigenvector (or eigenfunction) of the matrix (or operator) $H$.The Hamiltonian classically is the sum of the kinetic energy and the potential energy of the particles.
  • Philosophical Implications

    • Since its inception, many counter-intuitive aspects of quantum mechanics have provoked strong philosophical debates.
    • According to this interpretation, the probabilistic nature of quantum mechanics is not a temporary feature which will eventually be replaced by a deterministic theory, but instead must be considered a final renunciation of the classical idea of causality.
    • This is due to the quantum mechanical principle of wave function collapse.
    • One of the most bizarre aspect of the quantum mechanics is known as quantum entanglement.
    • Formulate the Copenhagen interpretation of the probabilistic nature of quantum mechanics
  • Diffraction

    • In classical physics, the diffraction phenomenon is described as the apparent bending of waves around small obstacles and the spreading out of waves past small openings.
    • As physical objects have wave-like properties (at the atomic level), diffraction also occurs with matter and can be studied according to the principles of quantum mechanics.
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