Schrödinger picture

The Schrödinger picture is the most familiar way of bookkeeping quantum dynamics: the state of the system carries the time dependence, while the operators that represent measurable quantities sit still. The wavefunction changes, spreads, and oscillates as the clock ticks, but the operator for, say, position or momentum is the same fixed object at every moment.

It is the picture most textbooks introduce first, and it matches our intuition that 'things change over time'. You watch the state vector swing around in its abstract space under the steady action of the time-evolution operator, and to predict a measurement at any instant you simply apply the unchanging operator to the current, evolved state.

It is essential to understand that this is a choice of bookkeeping, not a difference in physics. Whether you let the states move or let the operators move, every actual prediction — every probability, every average value — comes out identical. The Schrödinger picture and its alternatives are like describing a dance from the dancer's frame versus the floor's: same dance, different description.