Guys ,have u ever wondered what the white portion in a cube of ice is?water or a gas??
Plz reply,experts invited.
Erwin Schrödinger
Erwin Rudolf Josef Alexander Schrödinger ; 12 August 1887 – 4 January 1961) was an Austrian physicist who achieved fame for his contributions to quantum mechanics, especially the Schrödinger equation, for which he received the Nobel Prize in 1933. In 1935, after extensive correspondence with personal friend Albert Einstein, he proposed the Schrödinger's cat thought experiment.
FOR THOSE OF U WHO WONDERED WHERE THE SCHRODINGER EQUATION CAME FROM:::::::
Schrödinger's equation follows very naturally earlier developments:
In 1905, by considering the photoelectric effect, Albert Einstein had published his
formula for the relation between the energy E and frequency f of the quanta of radiation (photons), where h is Planck's constant.
In 1924 Louis de Broglie presented his de Broglie hypothesis which states that all particles (not just photons) have an associated wavefunction with properties:
, where is the wavelength of the wave and p the momentum of the particle.
De Broglie showed that this was consistent with Einstein's formula and special relativity so that
still holds, but now this is hypothesized to hold for all particles, not just photons anymore.
Expressed in terms of angular frequency and wavenumber , with we get:
and
where we have expressed p and k as vectors.
Schrödinger's great insight, late in 1925, was to express the phase of a plane wave as a complex phase factor:
and to realize that since
then
and similarly since:
and hence:
so that, again for a plane wave, he got:
And by inserting these expressions into the Newtonian formula for a particle with total energy E, mass m,moving in a potential V:
(simply the sum of the kinetic energy and potential energy; the plane wave model assumed V = 0)
he got his famed equation for a single particle in the 3-dimensional case in the presence of a potential:
Using this equation, Schrödinger computed the spectral lines for hydrogen by treating a hydrogen atom's single negatively charged electron as a wave, , moving in a potential well, V, created by the positively charged proton. This computation tallied with experiment, the Bohr model and also the results of Werner Heisenberg's matrix mechanics - but without having to introduce Heisenberg's concept of non-commuting observables. Schrödinger published his wave equation and the spectral analysis of hydrogen in a series of four papers in 1926.
The Schrödinger equation defines the behaviour of , but does not interpret what is. Schrödinger tried unsuccessfully to interpret it as a charge density. In 1926 Max Born, just a few days after Schrödinger's fourth and final paper was published, successfully interpreted as a probability amplitude, although Schrödinger was never reconciled to this statistical or probabilistic approach.
In the mathematical formulation of quantum mechanics, a physical system is associated with a complex Hilbert space such that each instantaneous state of the system is described by a ray in that space. The nonzero elements of a Hilbert space are by definition normalizable and it is convenient, although not necessary, to represent a state by an element of the ray which is normalized to unity. This vector is often somewhat loosely referred to as wave function, although in a more rigorous formulation of quantum mechanics a wave function is a special case of a state vector. (In fact, a wave function is a state in the position representation, see below). A state vector encodes the probabilities for the outcomes of all possible measurements applied to the system. It contains all information of the system that is knowable in a quantum mechanical sense. As the state of a system generally changes over time, the state vector is a function of time. The Schrödinger equation provides a quantitative description of the rate of change of the state vector.
In Dirac's bra-ket notation at time t the state is given by the ket . The time-dependent Schrödinger equation, giving the time evolution of the ket, is:
where i is the imaginary unit, t is time, d / dt is the derivative with respect to t, is the reduced Planck's constant (Planck's constant divided by ), is the time dependent state vector, and H(t) is the Hamiltonian (a self-adjoint operator acting on the state space). If one assumes a certain representation for , for instance position or momentum representation, the state vector is assumed to depend on more variables than time alone, and the time derivative must be replaced by the partial derivative
The Hamiltonian describes the total energy of the system. As with the force occurring in Newton's second law, its form is not provided by the Schrödinger equation, but must be independently determined from the physical properties of the system.
This is the third article in the series of The greatest physicists of all time:
The previous one were:
1. Isaac Newton.
2.Albert Einstein.
Plz Comment.
Hey if u see the order the no. of terms after which a digit's repetition ends is n+n-1+n-2=...........1.
eg:
3 ends after:3+2+1=6 terms and 4 ends after 4+3+2+1=10 terms..
Sum of n natural numbers is =n(n+1)/2..
Therefore for 1000: n(n+1)/2=1000 gives you n= 45.225 or -44.225.
Therefore 1000th term will be a 45.
PLZ RATE
Sir
I do not have a direct approach towards it,but analalytically I can be seen that as irrational quantities can not be exactly marked on the number line, it would be meaninful to call a function periodic with irrational period only when same values of f(x) occur at same difference of distances from the origin.
Plz reply soon.
A distinct function can have period = irrational quantity only when distance between the same values for f(x) is fixed ,even if irrational.
Here same values of f(x) are obtained at unequal intervals which is not a characteristic of a perodic function and therefore the function has to be constant.
Please reply as early as possible.
On a football ground in front of the oppostion goal,ready for a penalty kick,,,,,,,,,,,,,,,
At a barber's shop.....(Take it lightly man!)
ALBERT EINSTEIN
Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist. He is best known for his theory of relativity and specifically mass–energy equivalence, E = mc 2. Einstein received the 1921 Nobel Prize in Physics "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect."
Einstein's many contributions to physics include his special theory of relativity, which reconciled mechanics with electromagnetism, and his general theory of relativity, which was intended to extend the principle of relativity to non-uniform motion and to provide a new theory of gravitation. His other contributions include relativistic cosmology, capillary action, critical opalescence, classical problems of statistical mechanics and their application to quantum theory, an explanation of the Brownian movement of molecules, atomic transition probabilities, the quantum theory of a monatomic gas, thermal properties of light with low radiation density (which laid the foundation for the photon theory), a theory of radiation including stimulated emission, the conception of a unified field theory, and the geometrization of physics.
Einstein published over 300 scientific works and over 150 non-scientific works. Einstein is revered by the physics community, and in 1999 Time magazine named him the "Person of the Century". In wider culture the name "Einstein" has become synonymous with genius.
Einstein,1947.
Guys and gals,this one is second in the series of articles.The first on was on Sir Isaac Newton.
PLZ DO RATE............
The SAT Reasoning Test (formerly Scholastic Aptitude Test and Scholastic Assessment Test) is a standardized test for college admissions in the United States. The SAT is owned, published, and developed by the College Board, a non-profit organization in the United States, and was once developed, published, and scored by the Educational Testing Service (ETS).ETS now administers the exam.
The current SAT Reasoning Test is administered in about four hours and costs $45 ($71 International), excluding late fees. Since the SAT's introduction in 1901, its name and scoring has changed several times. In 2005, the test was renamed as "SAT Reasoning Test" with possible scores from 600 to 2400 combining test results from three 800-point sections (math, critical reading, and writing), along with other subsections scored separately.
SAT consists of three major sections: Critical Reading, Mathematics, and Writing. Each section receives a score on the scale of 200–800. All scores are multiples of 10. Total scores are calculated by adding up scores of the three sections. Each major section is divided into three parts. There are 10 sub-sections, including an additional 25-minute experimental or "equating" section that may be in any of the three major sections. The experimental section is used to normalize questions for future administrations of the SAT and does not count toward the final score. The test contains 3 hours and 45 minutes of actual timed sections,although most administrations, including orientation, distribution of materials, and completion of the biographical sections, run about 4 hours (10–25 minutes per sub-section) long.
Hey Kirti!
The answer is quite simple,provided u know the def. of critical velocity.
First for part 1:
To reach Point O(quarter circle)
mv2/2=mgR == v=;
Now for part 2:
Critical velocity is the velocity needed by a body at the bottommost point of a vertical circle,such that it continues circular motion at a point above the lower semicircle:
Therefore if in your problem a system with an object and a string is considered :
For angle t above lower semicircle:
mv2 /2=mgR(1+sint)+mgrsint/2.
(Note: For continuing circular motion: mgrsint=mv2 /R..)
Therfore solving we get:
Vc= (2gR+3gRsint)^1/2
Plz Rate.....
On earth
Thanks a lot
sporty ( i think)
