Download presentation

Presentation is loading. Please wait.

Published byElwin Booker Modified over 2 years ago

1
Operators - are performed on functions -are performed on vector functions and have directional qualities as well. These are referred to as vector operators. - can obey the Eigen equation, and thus have eigen values and eigen functions. - In general we are concerned with the function that obey this equation.

2
Classical Mechanics-Position Example Notice that we are using a function of time to describe the position not some fixed value. This function tells you the position at any point in time.

3
Classical Mechanics-Position-3D Note that the operator is applied to the position function and the result is the quantity associated with the operator. Ie. The x operator give you the x component of r(t), this is know as a projection operator. The vector operator r can be constructed from the projector operators.

4
Classical Mechanics-Position-3D Example

5
Classical Mechanics-Velocity-1D Example

6
Classical Mechanics-Velocity-3D Example

7
Classical Mechanics-Velocity-3D

8
The corresponding vector operator to velocity can be reconstructed from the projector operators of the components:

9
Classical Mechanics-Velocity-3D Example

10
Classical Mechanics-Acceleration-1D Example

11
Classical Mechanics-Acceleration-3D Example

12
Classical Mechanics-Force-1D Example

13
Classical Mechanics-Force-3D Example

14
Impulse and Momentum Momentum Impulse In general For a constant force

15
Momentum-1D Example

16
Momentum-3D Example

17
Impulse-1D Force can be thought of as a change in potential energy with change in position

18
Impulse-1D Examples i) In terms of the Force operator: ii) In terms of the Potential operator:

19
Impulse-3D

20
Angular Momentum

23
Kinetic Energy

24
Potential Energy Hooks Law Coulombs Law

25
Conservation of Energy Total energy remains constant, as long as V is not an explicit function of time. (i.e V(x(t))) Hamiltonian

26
Conservation of Energy-Hook’s Law Since: Newtons Law F – ma = 0

Similar presentations

Presentation is loading. Please wait....

OK

Work Readings: Chapter 11.

Work Readings: Chapter 11.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on nelson mandela biography Free ppt on moving coil galvanometer diagram Ppt on sweat equity shares Ppt on conservation of environment song Ppt on indian culture and tradition free download Ppt on new zealand culture for kids Ppt on teachers day wishes Ppt on sustainable development in bangladesh Ppt on 2nd world war flags Ppt online examination project documentation