What does the second derivative actually do in math and physics?

Ch 14: Where does the momentum operator come from? | Maths of Quantum Mechanics

Ch 13: Where does the Schrödinger equation come from? | Maths of Quantum Mechanics

Ch 12: What are generators in classical mechanics? | Maths of Quantum Mechanics

Ch 11: What are unitary operators? | Maths of Quantum Mechanics

Ch 10: What's the commutator and the uncertainty principle? | Maths of Quantum Mechanics

Ch 9: What are Hermitian operators? | Maths of Quantum Mechanics

Ch 8: Why is probability equal to amplitude squared? | Maths of Quantum Mechanics

Ch 7: How are observables operators? | Maths of Quantum Mechanics

Ch 6: What are bras and bra-ket notation? | Maths of Quantum Mechanics

Ch 5: What are Dirac deltas and wavefunction inner products? | Maths of Quantum Mechanics

Ch 4: What is an inner product? | Maths of Quantum Mechanics

Ch 3: Why do we need a Hilbert Space? | Maths of Quantum Mechanics

Ch 2: What are kets and wavefunctions? | Maths of Quantum Mechanics

Ch 1: Why linear algebra? | Maths of Quantum Mechanics