A/N: This is in homage to one of my favorite teachers. If you find it completely unfunny or confusing, just skip it as a specific-audience drabble. The idea came to me on the bus, after all. The equation Snape is looking at is at the end.
Severus Snape swept through the broken doorway and watched as torn pages fluttered aimlessly to the floor like brittle snowflakes.
His eyes fell on a page and he stopped, transfixed as by as basilisk's eyes – for there was the basilisk, a curving S shape. And what was this next to it, the thin little figure throwing its arms up in devotion – or despair?
"Ah, Severus." Lucius Malfoy stepped gingerly across the splintered threshold. Despite their robes and masks, they had no trouble telling each other apart now that the new recruits had gone on ahead. "Typical teenagers. They blew the whole library apart."
"Lucius – what is this?" Severus whispered, indicating the little figure with his wand.
Lucius stepped over for a closer look. "Why, I believe it's the complex conjugate," he drawled.
Severus sank to his knees.
"Goodness, Severus, are you that fond of maths?"
Severus didn't answer. The snake, the Dark Lord, was rearing over his supplicant – himself, Severus. He was certainly in a complex situation, but he'd only ever thought of having...conjugal...relations with Lily. That must be her, on the right, hair streaming behind her like it had done the day she'd jumped off of the swing on the playground. Between them, linking them together, but keeping them apart, was a large capital H. That must be H for Harry, Harry Potter. The boy's existence had been his mother's death. On the one hand he had separated Lily and Severus irrevocably, but on the other hand, the two had already parted ways by then. Severus' only remaining tie to Lily was that he had pledged his life to protect her son. How fitting that Severus should be pictured caught between Harry Potter and the Dark Lord.
A baleful star shone over the Severus figure. That was to be expected. He was nighttime and shadows; the bat of the dungeons; the spy; the Death Eater. Lily, however, had been sunshine and light. There was no ominous mark for her, but rather the letters "dr" – short for "dear," of course. Dear Lily.
Below the figure, the same scene was repeated, without Harry Potter. This must stand for the past. There was Severus again, in the middle between the snake of the Dark Lord on his left, and Lily, dear Lily, on his right. And, of course, he had chosen wrong.
"And this?" Severus croaked, tapping a large red E.
"The expectation value, I believe," Lucius sniffed. "Expectation value of energy."
Then it had been meant to be. A warm ray of hope pierced through the clouds of Severus' mind. His past mistakes and his present double life were expected. The power the Dark Lord knew not: that was energy, over time. Severus' sole purpose in life was to ensure that Harry Potter could grow up to face the Dark Lord. This whole nearly unbearable situation, the taut-wire web of deceit that cut him at every turn - this would produce energy, and energy over time was power.
Severus made a sharp motion with his wand, and the page flicked crisply over. There was the E again, safe within its walls, like the soothing cold stone of Hogwarts' dungeons. And now, lo and behold: Severus, and Harry, and Lily, encased in the same protective walls. No hissing basilisk gazed at Severus from the left, and no malevolent star hovered over Severus' brow from the right. Then, below them, as they had been at Hogwarts, were just Lily and Severus together. A thin wall separated them, but walls always had: the Fat Lady's portrait, for example. This was not important. What was important was that the Dark Lord's snake was no longer there. It could be done. They were not doomed. The arms on the Severus figure were raised in triumph.
Severus got briskly to his feet. "I've seen enough." With a curt wave of his wand, the book snapped shut.
"All right, then," Lucius said amiably. "Let's catch up with the others. You know, I had no idea you were interested in quantum mechanics. It astounds me that Muggles were able to come up with it on their own, since it is essential in really understanding transfiguration, for example. Of course, magic complicates it immensely..."
Severus had stopped listening. Instead, he was picturing the last figure that he'd seen: Severus and Lily, together, and safe. He slid the image behind his mental barriers, just in time to agree smoothly with Lucius that maths were quite lacking in the Hogwarts curriculum.
END
This is the equation Snape is looking at on the first page. Imagine that the integral sign is a lot bigger, the angle brackets are all a lot taller, and there is a division line between the numerator and denominator on the left
∫Ψ*HΨdr = ‹E›
∫ Ψ*Ψdr
and on the second page, in Dirac notation:
‹Ψ | H | Ψ› = ‹E›
‹Ψ | Ψ›
I think I got this all correct.