The Particle in a Box - A QM Model for Translation

Chapters 2-4 establish a framework for understanding physical systems in quantum mechanics.  This and the next few chapters will examine simple systems in the quantum mechanics framework.  The first system is the particle in a box, which can be used to model the translational motion of a particle.

1. Particle in a One-Dimensional Box

Here we discuss the problem of a particle moving freely along the x-axis between two points to show the origin of energy quantization.  Learn More.

2. Particle in a three-dimensional Box

We now can generalize the problem to 3D and introduce the concept of degeneracy.  Learn More.

3. Free Particle in 1D

In the particle in 1D box we learn that as the length of the box increases to infinity (e.g. free particle in 1D) the solution approach the classical limit.  Here we want to solve the free particle in 1D to varify that in fact the classical picture can be obtained.  Learn More.

4. Tunneling through a Barrier

Let us consider the case of a free particle moving with the total energy E encounters a barrier with the height %$V_0$% above E.  In classical mechanics, the particle will bounce back.  What happen to the particle in quantum mechanics?  Learn More.

5. Particle in a Finite Potential Well

Using what have learned from solving the problems above, we now can consider a more complex problem that is the particle in a 1D finite potential depth box.  It is different from the case of the particle in the infinite potential depth box where there are an infinite number of energy levels.  Here there are only a finite number of energy levels called bound states.  Learn More.

6. Applications of the Particle in a Box systems

Particle in a box system provides a simple model to understand a number of chemical properties such as:

1. Electrons in conjugated %$\pi$%-bond systems
2. Scanning Tunneling Microscopy (STM)
3. Tunneling in Chemical Reactions
4. Quantum wells or quantum dots

-- ThanhTruong - 12 Jul 2007