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I told my PChem (Quantum) class that it is perfectly fine for them to use online integrators like WolframAlpha . Many looked surprised and I was surprised about them being surprised. It's 2023, we don't use log tables etc. From a chemistry perspective calculating a complicated integral with paper&pencil seems like wasted time. Identifying integrals of odd fcts etc is a different story. How do you feel about this?
@SteinbockGroup I run Mathematica on my RasPi. Mainly because it's free, and it's fun. I don't see why chemists should be expected to know exactly how to integrate an equation. Their should know when integration is demanded to get an answer and find their own way to it. It's about the destination, not the journey.
@deadlyvices They all take Calculus I-II and often III here. I wish we replaced those with 'Math for Chemists' and include linear algebra, symbolic math, numerical methods, ... Much more powerful tools.
@SteinbockGroup Definitely linear algebra. Teach them what an eigenvector actually is and what it means. Start with simple rotations and reflections in three-space. Then move onto Hilbert space generalisation
@SteinbockGroup A rotation on a plane can be characterized by a perpendicular vector (lambda = 1). A reflection has lamba= -1.
Now just extend that argument to state vectors, such as spins...
@deadlyvices I have been going back and forth on introducing eigenvectors in PChem-II. Much more intuitive than eigenfunctions but there is only so much time. Would be nice if they had seen those things before.
@SteinbockGroup I've been brushing up my QM using Susskind's 'The Theoretical Minimum' lectures and book. It's a very good introduction, but QM still does my head in. The concepts are often extremely abstract.