Uploaded March 2015 | Updated September 2026, 3 weeks ago
The maths of quantum mechanics isn't actually hard. Plus you get to decide how far down the rabbit hole you want to tumble.
Error: at 3:55, one of the coefficients I wrote is 1/(4*sqrt(2)) + i/(4*sqrt(2)). Jiří Rožnovják pointed out that I did this calculation wrong, because as it stands, if you added the probability of each possible state, you don't get 1! The coefficient should be: 1/(sqrt(4*2)) + i/(sqrt(4*2))
The questions:
1. First a math one. If I have a complex number a+bi, use pythagoros’ rule to find the length of it. So what the probability of a state with this coefficient?
2. Then of course, an interpretations question. Many people have found the use of complex numbers in the wavefunction very significant, saying this shows that the wavefunction can’t actually be real then (literally. Ok, I need to stop.). In other words, if can’t be a real physical object. If so, what kinds of interpretations of the wavefunction would it rule out? But also, what do you think of this conclusion, that something described by complex numbers couldn’t actually represent ‘physical reality’? Are people taking the word imaginary too literally?
The maths of quantum mechanics isn't actually hard. Plus you get to decide how far down the rabbit hole you want to tumble.
Error: at 3:55, one of the coefficients I wrote is 1/(4*sqrt(2)) + i/(4*sqrt(2)). Jiří Rožnovják pointed out that I did this calculation wrong, because as it stands, if you added the probability of each possible state, you don't get 1! The coefficient should be: 1/(sqrt(4*2)) + i/(sqrt(4*2))
The questions:
1. First a math one. If I have a complex number a+bi, use pythagoros’ rule to find the length of it. So what the probability of a state with this coefficient?
2. Then of course, an interpretations question. Many people have found the use of complex numbers in the wavefunction very significant, saying this shows that the wavefunction can’t actually be real then (literally. Ok, I need to stop.). In other words, if can’t be a real physical object. If so, what kinds of interpretations of the wavefunction would it rule out? But also, what do you think of this conclusion, that something described by complex numbers couldn’t actually represent ‘physical reality’? Are people taking the word imaginary too literally?
