Quantum Mechanics Topodia - Build Your Expertise. Share it with the World

The Underlying Idea of the Schroedinger Equation but you may skip it, if you feel it tedious. We treat the motion of a free particle on which no force is exerted at all. Next, we discuss the case in which a force is exerted on a particle. Taking account of the double nature mentioned above, Schroedinger proposed a wave equation which the wave function for a free particle must obey; i.e. As alread...

http://www.kutl.kyushu-u.ac.jp/seminar/MicroWorld2_E/2Part1_E/2P13_E/Schroedinge...

Schrödinger Equation -- from Eric Weisstein's World of Physics

http://scienceworld.wolfram.com/physics/SchroedingerEquation.html

Quantum particles

The same relation is found for other types of particles. The above wave-length is called the de Broglie wave-length, after Louis de Broglie who first suggested that particles should have wave-like properties in 1923. Since the relation (45) between momentum and wave-number applies to both photons and massive particles, it seems plausible that the closely related relation (43) between energy and w...

http://farside.ph.utexas.edu/teaching/qmech/lectures/node23.html

Quantum particles

The same relation is found for other types of particles. The above wave-length is called the de Broglie wave-length, after Louis de Broglie who first suggested that particles should have wave-like properties in 1923. Since the relation (45) between momentum and wave-number applies to both photons and massive particles, it seems plausible that the closely related relation (43) between energy and w...

http://farside.ph.utexas.edu/teaching/qmech/lectures/node23.html

Meaning of wavefunction (English)

We therefore have to normalize the wave function so that it satisfies the normalization condition. Let be a solution of the Schroedinger equation. This total probability is obtained by integrating Eq. (1) over the whole space. A function obtained by multiplying an arbitrary non-zero constant C to the , i.e., , is also a wave function satisfying the same Schroedinger equation. The total probability...

http://www.kutl.kyushu-u.ac.jp/seminar/MicroWorld2_E/2Part1_E/2P15_E/wavefunctio...

Heisenberg - Quantum Mechanics, 1925-1927: Implications of Uncertainty

Heisenberg realized that the uncertainty relations had profound implications. For Einstein, this showed that quantum mechanics is "incomplete. Thus, for instance, the path of a particle has no meaning beyond the precision with which it is observed. Because the uncertainty relations are more than just mathematical relations, but have profound scientific and philosophical implications,...

http://www.aip.org/history/heisenberg/p08c.htm

Heisenberg's Quantum Mechanics (English)

As a result, the orbit of the electron is distorted. Heisenberg replaced the ordinary variables in classical mechanics with the matrix variables mentioned above and assumed the condition (4). The light collides with the electron as a particle with a given energy and momentum . Let the frequency and the wavelength of the light be and , respectively. Nowadays, these Heisenberg's matrix mechanics and...

http://www.kutl.kyushu-u.ac.jp/seminar/MicroWorld2_E/2Part1_E/2P14_E/Heisenberg_...

Heisenberg Uncertainty Principle

The HUP can be stated in different ways, let me first talk in terms of momentum and position. Suppose a particle has momemtum p and position x. In a Quantum Mechanical world, I would not be able to measure p and x precisely. This uncertainty leads to some strange effects. We do not know if this indeterminism is actually the way the Universe works, because the theory of Quantum Mechanics is proba...

http://zebu.uoregon.edu/~imamura/208/jan27/hup.html

Uncertainty principle

A perfect sinewave for the electron wave spreads that probability throughout all of space, and the "position" of the electron is completely uncertain. It no longer makes sense to say that you have precisely determined both the position and momentum of such a particle. Important steps on the way to understanding the uncertainty principle are wave-particle duality and the DeBroglie hypothesis. There...

http://hyperphysics.phy-astr.gsu.edu/Hbase/uncer.html

Bohr's theory and de-Broglie wave (English)

Bohr's quantum condition for a hydrogen atom. In Bohr's quantum theory, it is considered that an atom can be described by the Rutherford model of the nuclear atom, in which a heavy nucleus is surrounded by light electrons that move obeying the classical theory. The Rutherford Model of the Nuclear Atom A black big ball at the center is the nucleus and small red points moving around the nucleus are...

http://www.kutl.kyushu-u.ac.jp/seminar/MicroWorld2_E/2Part1_E/2P11_E/deBroglie_w...

Tunnel effect (English)

Let us assume the wave function to be As discussed above, this state is of a constant energy E . While the energy E can take a continuous value in the classical mechanics, it cannot be so in quantum mechanics. The alpha decay of atomic nuclei could be explained by a strange phenomenon called tunnel effect. We studied on the preceding page that "the probability density that a particle will be fo...

http://www.kutl.kyushu-u.ac.jp/seminar/MicroWorld2_E/2Part1_E/2P16_E/tunnel_effe...

Tunnel Effect

Since particles as well as light have particle-wave duality, matter (with an appropriate energy) can go through the wall according to quantum mechanics. De Broglie's idea of "matter as wave" suggests a startling consequence, and that's what is called the tunnel effect. But even when the particle has a lower energy than that, it can go through the wall, just as a wave can appear on the other side (...

http://www.bun.kyoto-u.ac.jp/~suchii/Bohr/tunnel.html

YouTube - What is quantum tunneling?

This video has been added to your favorites. Sign in with your Google Account! Hello, you either have JavaScript turned off or an old version of Adobe's Flash Player. James Bond: Quantum of Solace - Official traile. This will only change the interface, not any text entered by other users.

http://au.youtube.com/watch?v=6LKjJT7gh9s

Tunneling

The wave packet that tunneled through the potential barrier (i.e. Consider now a particle with energy E approaching a potential step of height V > E. Classically the particle would be reflected by the step. Qualitatively the tunnel effect does not depend on the shape of the potential barrier, as illustrated in the next animation for the case of a triangular barrier. Consider a classical particl...

http://msc.phys.rug.nl/quantummechanics/tunnel.htm

Schrodinger equation

Confining a particle to a smaller space requires a larger confinement energy. Since the wavefunction penetration effectively "enlarges the box", the finite well energy levels are lower than those for the infinite well. For a particle inside the box a free particle wavefunction is appropriate, but since the probability of finding the particle outside the box is zero, the wavefunction must go to ze...

http://www.mwit.ac.th/~physicslab/hbase/quantum/pbox.html

Particle in a box - Wikipedia, the free encyclopedia

In one dimension this amounts to the particle existing on a line segment, with the "walls" being the endpoints of the segment. There are also places within the box where the particle cannot ever be found. In other words, the least energy state of the system has a non-zero energy. In classical mechanics, the solution to the problem is trivial: The particle moves in a straight line, always at the sa...

http://en.wikipedia.org/wiki/Particle_in_a_box

The photoelectric effect

First, a given surface only emits electrons when the frequency of the light with which it is illuminated exceeds a certain threshold value, which is a property of the metal. Third, the energy of the photoelectrons is independent of the light intensity, but varies linearly with the light frequency. Suppose that an electron absorbs a single quantum of light. These facts are inexplicable within the f...

http://farside.ph.utexas.edu/teaching/qmech/lectures/node18.html

Quantum theory of light

http://farside.ph.utexas.edu/teaching/qmech/lectures/node19.html

Bohr theory (English)

The orbit of the electron in this case is elliptic in general. Thus, Bohr's quantum theory could beautifully reproduce the structure of the hydrogen atom. Then the electrons are subjected to a small retarding potential before being collected on the plate P. Then the quantum condition is written where a is the radius of the orbit. This means that the excitation energy of the mercury atom should...

http://www.kutl.kyushu-u.ac.jp/seminar/MicroWorld1_E/Part4_E/P43_E/Bohr_theory_E...

Quantum Mechanics

Build your expertise and Share it with the world