# Chapter 1: The Time Dependent Schrödinger Equation

The central object of study in this book is the Time Dependent Schrödinger Equation:

where is Planck's constant divided by 2π and is equal to 1.05450 x 10

erg sec, and H is the Hamiltonian operator:

In one dimension The function which satisfies this equation is called the wavefunction. According to the conventional interpretation of quantum mechanics, is the probability to find the particle between x and x + dx, assuming that is normalized, i.e.

In introductory classes, the Time Dependent Schrödinger Equation is usually solved by a separation of variables in position and time. The method of separation of variables leads naturally to particular solutions of the TDSE, which have the counterintuitive property of predicting time-independent observables. Only by considering superpositions of the particle solution can one observe time dependent behavior in quantum mechanics. A central tenet of this book is that these superposition solutions, or wavepackets, are both ubiquitous in nature as well as conceptually more transparent than the particular solutions.

where is Planck's constant divided by 2π and is equal to 1.05450 x 10

^{27}erg sec, and H is the Hamiltonian operator:

In one dimension The function which satisfies this equation is called the wavefunction. According to the conventional interpretation of quantum mechanics, is the probability to find the particle between x and x + dx, assuming that is normalized, i.e.

In introductory classes, the Time Dependent Schrödinger Equation is usually solved by a separation of variables in position and time. The method of separation of variables leads naturally to particular solutions of the TDSE, which have the counterintuitive property of predicting time-independent observables. Only by considering superpositions of the particle solution can one observe time dependent behavior in quantum mechanics. A central tenet of this book is that these superposition solutions, or wavepackets, are both ubiquitous in nature as well as conceptually more transparent than the particular solutions.