Scalars

We might start by thinking of scalars as being the simple numbers we use in grade school math. The word scalar refers to both real numbers and variables that hold real numbers.

A scalar holds a single value. This will stand out out once we start using math structures that hold two or more values.

The number 3 can be multiplied against 5 to make 15 and in so doing you have scaled 5 to something three times its original value.

When you get to Vectors and Matrices you will see how a scalar changes the scale of an object. We show a few examples below:

Vector

3 \begin{bmatrix} 1 \\2 \\3 \end{bmatrix} = \begin{bmatrix} 3 \\6 \\9 \end{bmatrix}

Matrix

3 \begin{bmatrix} a & b \\c & d \end{bmatrix} = \begin{bmatrix} 3a & 3b \\3c & 3d \end{bmatrix}

i\hbar\frac{\partial}{\partial t}\left|\Psi(t)\right>=H\left|\Psi(t)\right>