The Time Evolution of a Quantum System; or, My First Boyfriend

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When I start dating a quantum mechanical wave function, I know it’s not going to be easy. Sure, we’ll have our misunderstandings. Sure, we’ll raise some eyebrows. Sure, we’ll have to find ways to bridge that quantum/classical gap. But Ψ is just so quirky, so seductively unpredictable that I can’t help myself. What can I say? Surely I can’t be the only girl who finds a well-groomed, complex-valued probability amplitude irresistible.

Ψ takes me to a pizzeria on our first date. We share a pie and knocked back a few beers, and everything seems perfect. I tell him about my childhood dreams and he describes his penchant for commuting observables. Then, we go dancing. He whirls me around the dance floor with non-zero spin. After a few more drinks, I find myself flaunting my Newtonian assets and laughing at his dumb jokes about Young’s double slits. “Your basis or mine,” he whispers in my ear as the night wears on. “I’ll show you my hidden variables, if you show me yours.”


My mother takes the news about as well as one might expect. “Oy vey, a wave function?” she groans, pressing her hand to her temple to demonstrate the extent of her headache. “What’s wrong with someone like that nice boy who just moved in down the street from you? He looks...stable.”

She catches me rolling my eyes.

“You’re young,” she sighs. “Be careful.”


The problem with dating a wave function is the uncertainty. When you’re together, it’s great. But when you’re apart, you never know exactly where he is or how fast he’s moving. With a little effort, you can pin down one or the other, but never both at once. And when uncomfortable rumors start reaching your ears, it’s hard to get them out of your head.

Oo, they say, did you see Ψ and that little φ the other day? Those bras and kets were flying everywhere!

Yeah, they say, Ψ was in good form last night. Talk about a superposition of states!

Jeez, they say, is there any function Ψ won’t form a Hilbert space with?


I try to keep my cool, but eventually, it gets to me. “Am I not enough for you?” I demand the next time I catch up with him. “Seems like you’re all over the place these days.”

“C’mon, babe. I represent the random and discontinuous. It’s what I do! You can’t expect me to move in smooth, predictable patterns.”

“Is it my body? Am I too macroscopic?”

“Hey, what kinda variable quantity do you think I am?” he grins. “Amplitude has no physical significance to me, doll. It’s you I dig, classical curves and all.”

“But we never hold hands anymore. We never talk.”

Ψ smirks. “Sometimes you sound so Newtonian. Not that it’ s not a bad thing. You can’t help it.”

“What do you even mean?” I ask. “Sometimes I have no idea how to even interpret you! I mean, some of the things you do don’t even seem to correspond to real life!”

Ψ flutters a bit in the way he does when he’s getting impatient. “I may be complex-valued, baby, but this is going way over my head,” he says. “Wanna go cozy up somewhere and explore our inner products?”

“Back up,” I say. “Do you love me or not?”

“What?” Ψ asks, blinking.

“There are only two possibilities: yes or no.”

Ψ pauses for a long moment, then does what he does best. He oscillates.

“In some worlds I do,” he says, and I can tell from the tone of his voice that even he thinks the force of his response is weak.

“But what about in this one?” I ask.

When Ψ doesn’t reply, I lower my head and will my eyes to stop stinging.

“Babe,” he says, “don’t go analyzing things like this. If you make a measurement, you collapse the system, and we’ve got a pretty good thing going, right?”

I set my jaw and say quietly but firmly, “Just because you’re complex-valued doesn’t mean you get to be a jerk.”

Ψ’s probability amplitude ruffles into a shrug. “I need my degrees of freedom, doll,” he says. “I’m a function of them. But come on, that doesn’t mean we can’t have fun!”

I raise my eyes to look at Ψ one last time and he shoots me a gaze full of strangeness and charm. For a moment, I waver. In all his unfathomable glory, he embodies that bewitching combination of mystery and beauty. I’m on the brink of giving in, of losing my resolve, but then he opens his mouth. “Let’s go,” he says. “Let’s forget all this nonsense and go find ourselves a nice quiet place where we can merge our trajectories with some functional integration.”

“Goodbye, Ψ,” I say, as I turn away and start walking.


When I arrive at my parents’ house, my face is streaked with mascara. I feel good and not good at the same time. I use the key under the mat to let myself in and find my mother in the kitchen, frying onions and ground beef.

“Oh sweetheart,” she says when she sees me. “I’m sorry.”

“I thought you’d say, ‘I told you so’,” I say.

For a moment, she hesitates. Then she says softly, “Your father is a lovely man. I love him dearly and always have. But, one never forgets that first entanglement. It grips you, right? It holds you tight. Even over time. Even at a distance.”

“I should have listened to you,” I say.

My mother turns down the heat, then puts a hand on my shoulder. “Nah,” she says and smiles gently. “All we have to hold on to are the results of measurements we make. And, at the end of the day, each one of us has to run our own experiments.”

“I guess,” I say, but as the minutes pass, I’m already beginning to feel my memory of Ψ evolve.

About the Author: 
Ingrid Jendrzejewski grew up in Vincennes, Indiana, studied creative writing at the University of Evansville, then physics at the University of Cambridge. Links to Ingrid’s work can be found at and she tweets @LunchOnTuesday.