Derive schrodinger''s time dependent wave equation, Physics

Q. Derive Schrodinger's time dependent wave equation. What is the physical significance of wave function used in this equation?


Time Dependent Schrodinger's Equation : Let the wave function associated with a particle be represented where is the position vector and t is the time.

Now let us suppose that a particle is moving in +X direction then according to De-Broglie, there must be a wave associated with the moving particle. The wave function y, associated with the moving particle is given by

Physical interpretation of wave function : The quantity whose variation make up matter waves is called wave function. Normally wave function is represented by the symbol y. The wave function y, associated with a moving particle at the particular point x, y, z in space at the time t, gives the probability of finding the particle there at that time. The probability that something be in a certain place at a given time must lie between 0 and 1. An intermediate probability, say 0.2, means that there is a 20 % chance of finding the object. Now wave function y gives the amplitude of the wave and as we know that amplitude of any wave can either be positive or negative and a negative probability is meaningless. Hence y by itself cannot be an observable quantity or we can say that y has no direct physical significance.

There are certain basic postulates and essential definitions which are of fundamental importance.

1.    Wave function y is known as quantum mechanical state of the system as it describes a physical system completely.

2.    The intensity of a wave motion is proportional to the square of amplitude, so the intensity of the matter waves can also be defined by the square of its amplitude

3.    The wave function y can be expressed by a complex function. In that case it's complex conjugate is given by y and it is obtained by replacing each i by i.

4.    The probability of finding the particle in the interval dx around the point x at tim is dx. Similarly the probability of finding the particle in a volume element

5.    Normalization condition. This is called normalization condition. The wave function which satisfies above equation is said to be normalized to unity.

6.    Orthogonal wave function. Then these functions are said to be mutually orthogonal. This is known as orthogonality condition.

7.    The expectation value or average value of the physical observable quantity say Q is Defined as

8.    A wave function y must satisfy the following condition - wave function y and its first order derivative i.e. and must be finite, continuous, single valued everywhere and zero at large distances.

Posted Date: 7/11/2012 3:05:52 AM | Location : United States

Related Discussions:- Derive schrodinger''s time dependent wave equation, Assignment Help, Ask Question on Derive schrodinger''s time dependent wave equation, Get Answer, Expert's Help, Derive schrodinger''s time dependent wave equation Discussions

Write discussion on Derive schrodinger''s time dependent wave equation
Your posts are moderated
Related Questions
Is it possible to see your whole body in a flat, planar mirror that is LESS THAN half your height if the mirror is at an angle? (i.e. not parallel to your body)

Calculating unknown resistances The current through the galvanometer (G) - a very sensitive ammeter, is reduced to zero by adjusting R 4 .  The bridge is then said to be balanc

Q. Under fixed exchange rate, show using a figure, the effects of an expansionary fiscal policy. Show the equilibrium under a flexible exchange rate. Discuss the difference in t

Q. What are the applications of nmr spectroscopy? Answer:- The major applications of NMR stereoscopy are the elucidation of the carbon-hydrogen backbone of organic compoun

How is laser in treatment use as cooling? Lasers cooling treatment: A technique which has had recent success is laser cooling. It involves atom trapping, a process where a n

Intensities of an ordinary light and laser light The intensity (I) of a wave is the energy per unit time flowing through a unit normal area. The light from an ordinary light so

Q. Define: 1 amu One atomic mass unit is thinks as one twelfth of the mass of carbon atom 6 C 12 . 1 amu = 1.66 X 10 -27 kg. Q. Define: mass defect. The dissimi

Experiencing a constant horizontal 1.10 m/s wind, a hot-air balloon ascends from the launch site at a constant vertical speed of 2.70 m/s. At a height of 202 m, the balloonist main

Calculate mass of an electron accelerated to kinetic energy of 2 M eV.

Q. When the negative feedback is practical to an amplifier of gain 50 the gain falls to 25.  Compute the feedback ratio? Af = A / 1 + Aβ 25 = 50 / 1 + 50 β 1 = 2 / 1 + 50