• Learn how to write components of vectors in terms of the dot product
• Translate a problem given in terms of “arrows in space” to a problem in bra-ket notation
• Classical states vs. Quantum states

Estimated Time: 5-10 minutes

• Students should be familiar with Dirac notation
• Students should be familiar with the postulates of quantum mechanics

• Tabletop Whiteboard with markers

This activity can be split into two parts. The first part follows after an engaging conversation about how to tell a friend over the phone what kind of state vector one has. By the end of the conversation, students see how to write the components of an ordinary vector in terms of the dot product. To augment this lecture, students are then asked to use their small white boards to “retell” the story of the quantum friend in terms of bra-ket notation. For an example of how this activity can be implemented see Quantum Friend Act I, which also has an interesting extension afterward, seen in Quantum Friend Act II.

Students begin the second part of the activity after a brief summary of student responses to the first small white board question. This time the teacher explains she has a new friend, one with a quantum state, opposed to the classical state from before. Using the previous small white board question as motivation, students are asked to write particular symbols one would use to write down the probability that the vector is in a specific state. To see how this part of the activity could be implemented consider the following subtitled movie clip Quantum Friend Act III.