SCHRODINGERs WAVE EQUATION HEISENBERG UNCERTAINTY PRINCIPLE NOIDA INSTITUTE

SCHRODINGER’s WAVE EQUATION & HEISENBERG UNCERTAINTY PRINCIPLE NOIDA INSTITUTE OF ENGINEERING AND TECHNOLOGY GREATER NOIDA SUBMITTED BY: HARSH RAJ SUBMITTED TO: [ ] 1

SCHRONDINGER’s EQUATION #. The Schrodinger equation is the fundamental equation of physics for describing quantum mechanical behaviour. It is also often called the Schrodinger wave equation , and is a partial differential equation that describes how the wave function of a physical system evolves overtime. 2

GENERAL SOLUTION OF THE SCHRODINGER WAVE EQUATION The general form of the wave function is which also describes a wave moving in the x direction. In general the amplitude may also be complex. 3

TIME DEPENDENT SCHRODINGER’S WAVE EQUATION n The Schrodinger wave equation in its time dependent form for a particle of energy E moving in a potential V in one dimension is n The extension into three dimensions is 4

Time Independent Schrodinger Wave Equation Let the wave function for the wave is gives as: where A is amplitude of wave. K is wave number. The dependence on time and position can then be separated in the Schrodinger wave equation. , 5

n This is known as the time-independent Schrödinger wave equation, and it is a fundamental equation in quantum mechanics. 6

UNCERTAINTY PRINCIPLE The product of uncertainties in determining the position and momentum of the particle at the same time instant is at best of the order of. 7

where Is uncertainty in determining position of the particle. Is that in determining the momentum. Whenever a measurement is made there is always some uncertainty Quantum mechanics limits the accuracy of certain measurements because of wave –particle duality and the resulting interaction between the target and the detecting instrument. 8

The Heisenberg’s uncertainty principle When the momentum p is completely specified we write: and when the position x is completely unspecified we write: • In general, we always have: 9

So we can write: That is the Heisenberg’s uncertainty principle We also have for the particle moving in three dimensions: • With the definition of the constant 10

Thank You 11