The Schrodinger equation is a quantum physics partial differential equation used to determine the wave function and energy of atomic and molecular systems. It is a non-relativistic phenomenological equation that is solved to acquire insight into the qualities of a physical system. Calculation of an infinite set of linked integrodifferential equations is required in the general situation [3 ]. He found the electron in 1897, and that led to a model of an atom that had protons and electrons that had different charges. An experiment done by Ernest Rutherford and others in 1911 found that the positive charge in an atom was concentrated in space much smaller than the size of the atom itself. This is what they found. This led to a picture of the atom as a small solar system with a big, positively charged nucleus and a group of electrons that move around it all the time[4].
The Schrodinger equation is a quantum physics partial differential equation used to determine the wave function and energy of atomic and molecular systems. It is a non-relativistic phenomenological equation that is solved to acquire insight into the qualities of a physical system. Calculation of an infinite set of linked integrodifferential equations is required in the general situation [3 ]. He found the electron in 1897, and that led to a model of an atom that had protons and electrons that had different charges. An experiment done by Ernest Rutherford and others in 1911 found that the positive charge in an atom was concentrated in space much smaller than the size of the atom itself. This is what they found. This led to a picture of the atom as a small solar system with a big, positively charged nucleus and a group of electrons that move around it all the time[4].
The major problem in quantum physics is to find the wave function of a given physical system and to understand (predict) how the wave function of the system evolves in time, or how it changes under external influences. In 1926, Erwin Schrodinger predicted that the wave function of a given physical system might be completely determined if the total energy of the system was known. Since the equation represents a real physical system, it must satisfy the following conditions: the equation must be linear and coefficients appearing in this equation should only depend on the parameters characteristic of the particle. This chapter focuses on to the non-relativistic case only. It considers the case of a free particle moving in one dimension. The chapter shows that the Schrodinger equation can be obtained from the energy of the free particle. It shows that the Schrodinger equation guarantees the conservation of normalization of the wave function.
Quantum mechanics is the fundamental theory of nature at small scales and low energies of atoms and subatomic particles. Quantum mechanics is inescapable. Nearly all fields of modern physics, from elementary particles to the big bang, from semiconductors to solar energy cells, are related to quantum physics. Particles have characteristic trait of both particles and waves. The Schrodinger equation is the basic equation of quantum mechanics. The Schrodinger equation was established based on the quantization of energy conservation using quantum operators and the de Broglie relation. Wave function plays an important role in quantum mechanics. The probability interpretation assumes that the norm of the wave function measures the probability of the system in a particular coordinate or representation, in which the total probability is normalized.
The description of the physical and chemical properties of matter is a central issue that has occupied the minds of scientists since the age of the ancient Greeks. In their route to dissect matter down to what cannot be divided any further, they coined the term atom , the indivisible . Matter became then a collection of atoms. More than twenty centuries had to pass until the development of a more precise concept of atom, thanks, amongst others, to the systematic studies of Mendeleyev and the establishment in 1869 of the periodic table of the elements (Mendeleyev, 1869). The discovery of the electron in 1897 and the first modern model of the atomic structure by Sir Joseph Thomson were soon refined by his student, Sir Ernest Rutherford, who in 1910 showed that an atom was made of a positively charged small nucleus and a number of negatively charged electrons that neutralize the nuclear charge. Much in the spirit of planetary systems, and drawing from the analogy between gravitational and electrostatic interactions, scientists in the beginning of the twentieth century built an image of the atom that consisted of a number Z of electrons – of elementary charge – e – orbiting around the nucleus of charge Ze . A number of experimental observations, though, were incompatible with this idea of orbiting electrons. In particular, according to the successful electromagnetic theory, charged electrons in orbital (radially accelerated) motion should radiate energy, thus decelerating and eventually collapsing onto the nucleus. Clearly, such a picture would imply that matter is essentially unstable, in flagrant contradiction with our everyday experience of the very existence of matter.
As its name suggests, Schrodinger’s equation is the brain child of Schrodinger and was first disclosed in 1926 in a paper entitled An Undulatory Theory of the Mechanics of Atoms and Molecules . Schrodinger begins by considering the dynamics of a particle moving through a force field. The Schrodinger’s equation is arrived at in an alternative heuristic path modeled after Haken. The Schrodinger’s equation is a wave equation that incorporates classical particle concepts, and classical wave function concepts, in its derivation. In other words, a heuristic approach to Schrodinger’s equation utilizes Max Planck’s quantum energy, classical kinetic energy of a free particle, and the classical “wave functions of ordinary wave optics.” Schrodinger’s equation is capable of explaining all atomic phenomena except those involving magnetism and relativity.
Something is rotten in the state of Denmark. Shakespeare , Hamlet, Act 1 Scene 4 The rise and fall of the old quantum theory The principles of the old quantum theory were first articulated by Niels Bohr in 1913 in a three-part paper titled “On the Constitution of Atoms and Molecules.” Bohr had adopted Ernest Rutherford's model of the atom, according to which the mass of the atom is concentrated in a small central nucleus, while the electrons orbit the nucleus in planetary trajectories. The key challenge facing Rutherford's model was that it was unstable: according to classical electrodynamics, the electron, which is a moving charged body, should radiate energy and so eventually collapse into the nucleus. Bohr's solution was to incorporate Max Planck's theory of radiation, according to which “the energy radiation from an atomic system does not take place in the continuous way assumed in ordinary electrodynamics, but that it, on the contrary, takes place in distinctly separated emissions” (Bohr 1913, p. 4; BCW 2, p. 164). In this early paper, and most subsequent accounts, Bohr summarized his quantum theory by means of two assumptions or postulates. According to the first postulate, electrons cannot travel in any path they like around the nucleus, rather atomic systems can only exist in a series of discrete “stationary states,” in which the electron is in a particular allowed stable periodic orbit and is not emitting radiation.