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Shrodinger's crouch (Also often refered to as "Quantum Crouch") is a Glitch present in HL2-Based games running on Source 2009 or later which allows the player to crouch, while keeping their camera in the standing position. This allows the camera to go through brushes, as nothing is stopping it from doing so.
Quantum crouching replaces CEOOB, which was patched at the same time.
When the player crouches, then uncrouches, and crouches again before the animation of standing up completes, the game glitches their stance into two states. The camera becomes seperated from the player's actual body, allowing the player to peek their view through ceilings. The player's shots and use presses still come from the camera, and NPCs will still try to aimt at it.
The player is unable to jump while in a Schrodinger's Crouch, and it can prove to be difficult to reach a high ceiling. Gaining height without jumping in half-life 2 is usually done by punting an object under the player with the gravity gun, and in portal by manipulating portals.
The player must also be fully uncrouched on the ground before performing a quantum crouch. If the player tries to jump, crouch mid air, and then perform a shrodinger's crouch once on the ground, the game will simply ignore the input.
Simply crouch, then uncrouch, and while the standup animation occurs, crouch again. Your camera will freeze in place, and how late you crouch in the animation determines the height at which the camera will freeze.
Quantum Crouching is useful for shooting, and activating buttons through ceilings.
It can also be used to cleverly dodge the shots of the NPCs, as they will always aim to shoot the camera instead of the player body
Another use is in Portal, where the player can peek their head out of a ceiling to shoot a portal Out of Bounds. It can also be used to enter a portal at the edge to clip your view above where you could normally. This is done by performing it at a platform that you would need to crouch to get under. If you have a portal on the underside, then your view should go to the other portal.