Complex wavefunctions

Volker Schmidt

Steve Spicklemire

O NE OF the most basic ideas of quantum mechanics is that the condition of a system is represented mathematically by a wavefunction . This is a complex valued mathematical function of that tells us everything we can know about the system. In order to make predictions we apply mathematical operations to the wavefunction that tell us the probability of various outcomes that we can compare to experimental results. The wavefunction is a complex valued function. In other words when you evaluate it for a particular set of inputs (e.g., position, time, momentum, energy, etc.) the output is a complex number. The magnitude of the complex number gives information about the relative likelihood of a particular outcome. That seems pretty odd I'm sure. The best way to get comfortable with the notion is to play around with it. Let's consider an example.

Philippe A. Martin

Jincheng Zhang

This paper introduces Hyperdimensional Wavefunction Collapse (HWC), a novel method for generating highly complex and diverse wavefunctions. We propose a dynamically collapsing algorithm that generates wavefunctions at multiple scales, combining them to produce intricate patterns. The core of HWC lies in its multi-scale, adaptive approach, which significantly enhances sampling efficiency and versatility compared to existing methods. We detail the algorithm's design, the resulting wave function generation process, and the resulting impact on wave function diversity. This work demonstrates the potential of HWC to produce complex wavefunctions with improved efficiency and adaptability.

Sacha Cerf, Clara Wassner, Jack Davis +2 more

The Schrödinger wavefunction is ubiquitous in quantum mechanics, quantum chemistry, and bosonic quantum information theory. Its zero-set for fermionic systems is well-studied and central for determining chemical properties, yet for bosonic systems the zero-set is less understood, especially in the context of characterizing non-classicality. Here we study the zeros of such wavefunctions and give them a novel information-theoretic interpretation. Our main technical result is showing that the wavefunction of most bosonic quantum systems can be extended to a holomorphic function over the complex plane, allowing the application of powerful techniques from complex analysis. As a consequence, we prove a version of Hudson's theorem for the wavefunction and characterize Gaussian dynamics as classical motion of the wavefunction zeros. Our findings suggest that the non-Gaussianity of quantum optical states can be detected by measuring a single quadrature of the electromagnetic field, which we demonstrate in a companion paper [arXiv:2507.23005]. More generally, our results show that the non-Gaussian features of bosonic quantum systems are encoded in the zeros of their wavefunction.