Scalars
- Define a scalar.
- Perform the following operations between scalars: addition, subtraction, multiplication, division.
- Simplify expressions through factorization and distribution.
- Write code in Python or another language to perform calculations with scalars.
Complex Numbers
- Define a complex number and label the real and complex components.
- Define the imaginary number, i.
- Perform addition, subtraction, and multiplication with complex numbers.
- Calculate the complex conjugate, modulus, and modulus squared for a given complex number.
- Define a complex number in Python and perform calculations with it.
Vectors
- Define a vector, determine its size, and label the elements.
- Calculate the magnitude and unit vector for a given vector.
- Perform addition and subtraction between two vectors and scalar multiplication and division with a vector and a scalar.
- Calculate the dot product between two vectors and use the dot product to determine the angle between the vectors.
- Describe, geometrically, what the result of taking the cross product between two vectors is.
- Describe the difference between a bra and a ket and how to convert between the two representations.
- Write and calculate dot products using Dirac notation.
- Define vectors in Python using Numpy arrays and perform basic calculations with them.
Matrices
- Define a matrix.
- Perform addition and subtraction between two matrices and scalar multiplication and division with a matrix and a scalar.
- Define the commutator between two matrices.
- Calculate the transpose, conjugate, and transpose between two matrices.
- Show a matrix in Dirac notation with bras and kets.
- Define matrices in Python using Numpy arrays and perform basic calculations.