Tampilkan postingan dengan label Quantum Mechanics. Tampilkan semua postingan
Tampilkan postingan dengan label Quantum Mechanics. Tampilkan semua postingan

Selasa, 01 September 2009

Fisika Modern

In the mathematically rigorous formulation of quantum mechanics developed by Paul Dirac[8] and John von Neumann,[9] the possible states of a quantum mechanical system are represented by unit vectors (called "state vectors"). Formally, these reside in a complex separable Hilbert space (variously called the "state space" or the "associated Hilbert space" of the system) well defined up to a complex number of norm 1 (the phase factor). In other words, the possible states are points in the projective space of a Hilbert space, usually called the complex projective space. The exact nature of this Hilbert space is dependent on the system; for example, the state space for position and momentum states is the space of square-integrable functions, while the state space for the spin of a single proton is just the product of two complex planes. Each observable is represented by a maximally Hermitian (precisely: by a self-adjoint) linear operator acting on the state space. Each eigenstate of an observable corresponds to an eigenvector of the operator, and the associated eigenvalue corresponds to the value of the observable in that eigenstate. If the operator's spectrum is discrete, the observable can only attain those discrete eigenvalues.

In the formalism of quantum mechanics, the state of a system at a given time is described by a complex wave function, also referred to as state vector in a complex vector space.[10] This abstract mathematical object allows for the calculation of probabilities of outcomes of concrete experiments. For example, it allows one to compute the probability of finding an electron in a particular region around the nucleus at a particular time. Contrary to classical mechanics, one can never make simultaneous predictions of conjugate variables, such as position and momentum, with accuracy. For instance, electrons may be considered to be located somewhere within a region of space, but with their exact positions being unknown. Contours of constant probability, often referred to as "clouds", may be drawn around the nucleus of an atom to conceptualize where the electron might be located with the most probability. Heisenberg's uncertainty principle quantifies the inability to precisely locate the particle given its conjugate momentum.[11]


Fig. 1: Probability densities corresponding to thewavefunctions of an electron in a hydrogen atompossessing definite energy levels (increasing from the top of the image to the bottom: n = 1, 2, 3, ...) andangular momentum (increasing across from left to right:s, p, d, ...). Brighter areas correspond to higher probability density in a position measurement. Wavefunctions like these are directly comparable toChladni's figures of acoustic modes of vibration inclassical physics and are indeed modes of oscillation as well: they possess a sharp energy and thus a keenfrequency. The angular momentum and energy arequantized, and only take on discrete values like those shown (as is the case for resonant frequencies in acoustics).



Lecture 6 of Leonard Susskind's Modern Physics course concentrating on Quantum Mechanics. Recorded February 18, 2008 at Stanford University.


This Stanford Continuing Studies course is the second of a six-quarter sequence of classes exploring the essential theoretical foundations of modern physics. The topics covered in this course focus on quantum mechanics. Leonard Susskind is the Felix Bloch Professor of Physics at Stanford University.Complete playlist for the course:http://youtube.com/view_play_list?p=189C0DCE90CB6D81Stanford Continuing Studies: http://continuingstudies.stanford.edu/About Leonard Susskind:http://www.stanford.edu/dept/physics/people/faculty/susskind_leonard.htmlStanford University channel on YouTube:http://www.youtube.com/stanford

Kategori:

Pendidikan


Course material
Diposting oleh di Tidak ada komentar:
Label: , ,

Jumat, 28 Agustus 2009

Fisika Modern

The word quantum derives from Latin, meaning "how great" or "how much".[4] In quantum mechanics, it refers to a discrete unit that quantum theory assigns to certain physical quantities, such as the energy of an atom at rest. The discovery that particles are discrete packets of energy with wave-like properties led to the branch of physics dealing with atomic and sub-atomic systems which is today called quantum mechanics. It is the underlying mathematical framework of many fields of physics and chemistry, including condensed matter physics, solid-state physics, atomic physics, molecular physics, computational physics, computational chemistry, quantum chemistry,particle physics, nuclear chemistry, and nuclear physics.[5] Some fundamental aspects of the theory are still actively studied.[6]

Quantum mechanics is essential to understand the behavior of systems at atomic length scales and smaller. For example, if classical mechanics governed the workings of an atom, electrons would rapidly travel towards and collide with the nucleus, making stable atoms impossible. However, in the natural world the electrons normally remain in an uncertain, non-deterministic "smeared" (wave–particle wave function) orbital path around or through the nucleus, defying classical electromagnetism.[7]

Quantum mechanics was initially developed to provide a better explanation of the atom, especially the differences in the spectra of lightemitted by different isotopes of the same element. The quantum theory of the atom was developed as an explanation for the electron remaining in its orbit, which could not be explained by Newton's laws of motion and Maxwell's laws of classical electromagnetism.

Broadly speaking, quantum mechanics incorporates four classes of phenomena for which classical physics cannot account:



Lecture 5 of Leonard Susskind's Modern Physics course concentrating on Quantum Mechanics. Recorded February 11, 2008 at Stanford University.

This Stanford Continuing Studies course is the second of a six-quarter sequence of classes exploring the essential theoretical foundations of modern physics. The topics covered in this course focus on quantum mechanics. Leonard Susskind is the Felix Bloch Professor of Physics at Stanford University.

Complete playlist for the course:
http://youtube.com/view_play_list?p=189C0DCE90CB6D81

Stanford Continuing Studies: http://continuingstudies.stanford.edu/

About Leonard Susskind

Course material
Diposting oleh di Tidak ada komentar:
Label: , ,

Jumat, 14 Agustus 2009

Fisika Modern

Historically, the earliest versions of quantum mechanics were formulated in the first decade of the 20th century at around the same time as the atomic theory and the corpuscular theory of light as updated by Einstein first came to be widely accepted as scientific fact; these latter theories can be viewed as quantum theories of matter and electromagnetic radiation. Quantum theory was significantly reformulated in the mid-1920s away from the old quantum theory towards the quantum mechanics formulated by Werner Heisenberg, Max Born, Wolfgang Pauli and their associates, accompanied by the acceptance of the Copenhagen interpretation of Niels Bohr. By 1930, quantum mechanics had been further unified and formalized by the work of Paul Dirac and John von Neumann, with a greater emphasis placed on measurement in quantum mechanics, the statistical nature of our knowledge of reality and philosophical speculation about the role of the observer. Quantum mechanics has since branched out into almost every aspect of 20th century physics and other disciplines such as quantum chemistry, quantum electronics, quantum optics and quantum information science. Much 19th century physics has been re-evaluated as the classical limit of quantum mechanics, and its more advanced developments in terms of quantum field theory, string theory, and speculative quantum gravity theories. (Wikipedia)


Lecture 3 of Leonard Susskind's Modern Physics course concentrating on Quantum Mechanics. Recorded January 28, 2008 at Stanford University.

This Stanford Continuing Studies course is the second of a six-quarter sequence of classes exploring the essential theoretical foundations of modern physics. The topics covered in this course focus on quantum mechanics. Leonard Susskind is the Felix Bloch Professor of Physics at Stanford University.

Complete playlist for the course:
http://youtube.com/view_play_list?p=189C0DCE90CB6D81

Stanford Continuing Studies: http://continuingstudies.stanford.edu/

About Leonard Susskind: http://www.stanford.edu/dept/physics/people/faculty/sussk...

Stanford University channel on YouTube:
http://www.youtube.com/stanford


Course material
Diposting oleh di Tidak ada komentar:
Label: ,

Selasa, 04 Agustus 2009

Fisika Modern


The mathematical formulations of quantum mechanics are abstract. Similarly, the implications are often non-intuitive in terms of classic physics. The centerpiece of the mathematical system is the wavefunction. The wavefunction is a mathematical function providing information about the probability amplitude of position and momentum of a particle. Mathematical manipulations of the wavefunction usually involve the bra-ket notation, which requires an understanding of complex numbers and linear functionals. The wavefunction treats the object as a quantum harmonic oscillator and the mathematics is akin to that of acoustic resonance. Many of the results of quantum mechanics do not have models that are easily visualized in terms of classical mechanics; for instance, the ground state in the quantum mechanical model is a non-zero energy state that is the lowest permitted energy state of a system, rather than a more traditional system that is thought of as simply being at rest with zero kinetic energy.
(Wikipedia)



Lecture 2

This Stanford Continuing Studies course is the second of a six-quarter sequence of classes exploring the essential theoretical foundations of modern physics. The topics covered in this course focus on quantum mechanics. Leonard Susskind is the Felix Bloch Professor of Physics at Stanford University.

Complete playlist for the course:
http://youtube.com/view_play_list?p=189C0DCE90CB6D81

Stanford Continuing Studies: http://continuingstudies.stanford.edu/

About Leonard Susskind: http://www.stanford.edu/dept/physics/people/faculty/sussk...

Stanford University channel on YouTube:
http://www.youtube.com/stanford

Course material
Diposting oleh di Tidak ada komentar:
Label: ,

Sabtu, 04 Juli 2009

Fisika Modern

Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic scales, the so-called quantum realm. In advanced topics of quantum mechanics, some of these behaviors are macroscopic and only emerge at very low or very high energies or temperatures. The name, coined by Max Planck, derives from the observation that some physical quantities can be changed only by discrete amounts, or quanta, as multiples of the Planck constant, rather than being capable of varying continuously or by any arbitrary amount. For example, the angular momentum, or more generally the action, of an electron bound into an atom or molecule is quantized. While an unbound electron does not exhibit quantized energy levels, an electron bound in an atomic orbital has quantized values of angular momentum. In the context of quantum mechanics, the wave–particle duality of energy and matter and the uncertainty principle provide a unified view of the behavior of photons, electrons and other atomic-scale objects.




Lecture 1 of Leonard Susskind's Modern Physics course concentrating on Quantum Mechanics. Recorded January 14, 2008 at Stanford University.

This Stanford Continuing Studies course is the second of a six-quarter sequence of classes exploring the essential theoretical foundations of modern physics. The topics covered in this course focus on quantum mechanics. Leonard Susskind is the Felix Bloch Professor of Physics at Stanford University.

Complete playlist for the course:
http://youtube.com/view_play_list?p=189C0DCE90CB6D81

Stanford Continuing Studies: http://continuingstudies.stanford.edu/

About Leonard Susskind: http://www.stanford.edu/dept/physics/people/faculty/sussk...

Stanford University channel on YouTube:
http://www.youtube.com/stanford
Diposting oleh di Tidak ada komentar:
Label: ,
Langganan: Postingan (Atom)