1: The Quantum Particle
- Page ID
- 44688
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We will begin by introducing the tools from quantum mechanics that we will need to describe electrons. We will introduce probabilistic descriptions of the key physical properties: position, momentum, time and energy. In the next part we will consider electrons in the simplest possible model of a conductor – a box – i.e. we will ignore atoms and assume that the material is perfectly homogeneous. This model of electrons in conductors is known as "the particle in a box‟. It is surprisingly useful, and later in the class we will employ it to describe the behavior of modern transistors.
- 1.7: The Wavefunction
- Following the conventions of quantum mechanics, we will define a function known as the wavefunction, ψ(x,t) , to describe the electron. It is typically a complex function and it has the important property that its magnitude squared is the probability density of the electron at a given position and time.