Why is a QM wave function not normalizable

Ed Quanta
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In quantum mechanics, why is a wave function not normalizable if it always has the same sign as its second derivative?
 
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In 1D, if f"/f is positive, the function curves away from the x axis.
To be normalizable, it must in some region curve toward the x axis.
 
Ed Quanta said:
In quantum mechanics, why is a wave function not normalizable if it always has the same sign as its second derivative?

Your question doesn't make (too much) sense, since a wave function is a complex (generally with a nonzero imaginary part) valued function and to say that a+ib >0 makes no sense.
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
If we release an electron around a positively charged sphere, the initial state of electron is a linear combination of Hydrogen-like states. According to quantum mechanics, evolution of time would not change this initial state because the potential is time independent. However, classically we expect the electron to collide with the sphere. So, it seems that the quantum and classics predict different behaviours!

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