By Sunil Bhardwaj

4858 Views

An operator is a symbol for a certain mathematical procedure which transforms one function to another.

In other words,

An operator is an instruction to carry out certain operations.

For every physical measurable or observable quantity like position, velocity, linear momentum, angular momentum, energy of the system, there is a corresponding operator in quantum mechanics.

Linear Operator:

While operating on the sum of two functions (f and g), if an operator $$(\widehat { A } )$$ gives the same result as the sum of the operations on the two functions seperately, then the operator is said to be linear.

Suppose f and g are two functions and $$\widehat { A }$$ is an operator then if, $$\widehat { A } \left( f + g \right) = \widehat { A } f + \widehat { A } g$$ the operator is linear operator.

Vector Operator:

When a vector quantity like momentum is converted into operator, it becomes a vector operator. This vector operator can be obtained in terms of Cartesian Coordinates (x, y and z directions) by following relation. $$\triangledown = i\frac { \partial }{ \partial x } + j\frac { \partial }{ \partial y } + k\frac { \partial }{ \partial z }$$ where, i, j and k are the unit vectors along the x, y and z coordinates.

#### Latest News

• Become an Instructor 4 March, 2018

Apply to join the passionate instructors who share their expertise and knowledge with the world. You'll collaborate with some of the industry's best producers, directors, and editors so that your content is presented in the best possible light..

#### More Chapters

• Spectroscopy
• Basic Quantum Chemistry
• Phase Rule
• Electrochemistry
• Colloidal State
• Chemical Thermodynamics
• Gaseous State
• Applied Electrochemistry
• Ionic Equilibria
• Nuclear Chemistry
• Solid State Chemistry
• Chemical Kinetics
• #### Other Subjects

• English
• Applied Physics
• Environmental Studies
• Physical Chemistry
• Analytical Chemistry
• Organic Chemistry
• Soft Skills
• Engineering Drawing
• General Medicine
• Mathematics
• Patente B Italia