Summary
- Debroglie wavelength: A particle of mass m moving with velocity v has a wavelength λ related to the momentum p = mv by., λ = h/p. This wavelength, λ, is known as the de Broglie wavelength of the particle (where h is Planck's constant). Since the value of Planck's constant is incredibly small h = 6.634 × 10 − 34, the wavelike nature of everyday objects is not really observable. Suppose an electron at rest has been accelerated through a potential difference of V volts and gains a velocity v. If m and e are the mass and charge of electron respectively, then Work done on electron, E = e, then the Debroglie wavelength of an electron is
- Davisson – Germer Experiment: The hypothesis says that the particles of matter such as electrons have wave like properties. This experiment demonstrated the wave nature of the electron, confirming the earlier hypothesis of deBroglie. Putting wave – particle duality on a firm experimental footing, it represented a major step forward in the development of quantum mechanics. The Bragg law for diffraction had been applied to x – ray diffraction, but this was the first application to particle waves.
- Schrodinger wave function: Wave function Ψ is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves. Probability amplitude is a complex number whose modulus squared represents a probability or probability density. Although Ψ is a complex number, |Ψ|2 is real, and corresponds to the probability density of finding a particle in a given place at a given time, if the particle's position is measured. There are two different Schrodinger equations: (1) Time Dependent and
(2) Time Independent Schrodinger equation. In general the Time Dependent Schrodinger equation gives the total information about the system.
- Uncertainty Principle: It is impossible to determine both momentum
and position by means of the same measurement. While measuring, each interaction will alter its momentum
by an unknown and indeterminable increment, degrading our knowledge of its momentum while augmenting
our knowledge of its position. So argues that every measurement destroys part of our knowledge of the
system that was obtained by previous measurements.
- Electron Spin: The electron doesn't physically spin about any axis, it possesses a mysterious angular momentum (h / 2). The electron has an additional degree of freedom excluding the three associated with position (x, y, z) of space. The coordinate associated with the new degree of freedom can only take two values +1/2 and − 1/2.
- Dirac Equation: Although Schrodinger had previously discovered an equation that describes the movement of the electron, his equation does not take the theory of relativity into consideration. The Dirac equation is a system of four equations related to each other. This is because the operator associated with the Dirac equation is a differential matrix operator. It describes a wave system that is dispersed in time and space. It describes fields corresponding to elementary spin – 1/2 particles (such as the electron).