with graduate students who have had the undergraduate course, but are unable to sketch wave functions for an arbitrarily drawn potential energy function. We think that such a skill is crucial for understanding quantum mechanics at the introductory level and, thus, we spend a good deal of Chapter 2 discussing qualitative aspects of the wave function In Chapter 3 we solve the Schrodinger equation for two of the most important po- tential energy functions, the infinite square well and the harmonic oscillator. A point of contrast between the these potentials is penetration of oscillator wave functions into the classically forbidden region. We discuss this penetration at length because, in our experience, students have a great deal of difficulty with this concept. We then elaborate upon this concept by presenting the details of a problem not often seen in elementary texts, an infinite square well with a barrier in the middle. This affords at, for energies less than the barrier height, the part can be found on either side of the classically impenetrable barrier, thus making the article's presence inside the barrier undeniable. This problem also sets the stage for solution of the more conventional barrier penetration problems in Chapter 5 In Chapter 4 we discuss time-dependent states. We choose to do this at this poi contrast these states with those studied in the previous chapter. While we discuss the free particle wave packet(as does virtually every other text), we also present wave packets under the influence of a constant force and of a harmonic force. This discussion will, we believe, relate nicely to a later presentation of harmonic oscilla- tor coherent states( Chapter 7) Chapter 5 is an extension of Chapter 3 in that we solve the time-independer Schrodinger equation for several different one-dimensional potential energies. In- cluded is one of the most successful analytic potential energy functions for charac- terizing diatomic molecular vibrations, the Morse potential. The chapter concludes with the WKB method for approximating solutions Chapter 6 presents the formalism of quantum physics, the mechanic tum mechanics, including a set of postulates For completeness we also discuss the Schrodinger and Heisenberg pictures. Chapter 7 is devoted to the operator solu tion of the Schrodinger equation for the harmonic oscillator with emphasis on the properties of the ladder operators. Harmonic oscillator coherent states are also dis- cussed. Chapter 8 introduces three-dimensional problems and is devoted to angular momentum. It is emphasized in this chapter that the concept of angular momen- tum in quantum mechanics transcends three-dimensional rotations (orbital angular momentum) Chapters 9 and 10 are devoted to solving the radial Schrodinger equation for everal different central potentials. In addition to the common central potentials Chapter 9 includes a thorough discussion of the isotropic harmonic oscillator using the shell model of the nucleus as an example. The isotropic oscillator also permits introduction the concept of accidental degeneracy. Because they are constituents of oscillator eigenfunctions, an attempt is made to decrypt the different conventions that are used for Laguerre polynomials and associated Laguerre polynomials In our experience, this is a source of confusion to many students. Also contained this chapter is an elaboration on the Morse potential in which three-dimensionalviii Preface with graduate students who have had the undergraduate course, but are unable to sketch wave functions for an arbitrarily drawn potential energy function. We think that such a skill is crucial for understanding quantum mechanics at the introductory level and, thus, we spend a good deal of Chapter 2 discussing qualitative aspects of the wave function. In Chapter 3 we solve the Schr¨odinger equation for two of the most important po￾tential energy functions, the infinite square well and the harmonic oscillator. A point of contrast between the these potentials is penetration of oscillator wave functions into the classically forbidden region. We discuss this penetration at length because, in our experience, students have a great deal of difficulty with this concept. We then elaborate upon this concept by presenting the details of a problem not often seen in elementary texts, an infinite square well with a barrier in the middle. This affords the opportunity to see that, for energies less than the barrier height, the particle can be found on either side of the classically impenetrable barrier, thus making the particle’s presence inside the barrier undeniable. This problem also sets the stage for solution of the more conventional barrier penetration problems in Chapter 5. In Chapter 4 we discuss time-dependent states. We choose to do this at this point to contrast these states with those studied in the previous chapter. While we discuss the free particle wave packet (as does virtually every other text), we also present wave packets under the influence of a constant force and of a harmonic force. This discussion will, we believe, relate nicely to a later presentation of harmonic oscilla￾tor coherent states (Chapter 7). Chapter 5 is an extension of Chapter 3 in that we solve the time-independent Schr¨odinger equation for several different one-dimensional potential energies. In￾cluded is one of the most successful analytic potential energy functions for charac￾terizing diatomic molecular vibrations, the Morse potential. The chapter concludes with the WKB method for approximating solutions. Chapter 6 presents the formalism of quantum physics, the mechanics of quan￾tum mechanics, including a set of postulates. For completeness we also discuss the Schr¨odinger and Heisenberg pictures. Chapter 7 is devoted to the operator solu￾tion of the Schr¨odinger equation for the harmonic oscillator with emphasis on the properties of the ladder operators. Harmonic oscillator coherent states are also dis￾cussed. Chapter 8 introduces three-dimensional problems and is devoted to angular momentum. It is emphasized in this chapter that the concept of angular momen￾tum in quantum mechanics transcends three-dimensional rotations (orbital angular momentum). Chapters 9 and 10 are devoted to solving the radial Schr¨odinger equation for several different central potentials. In addition to the common central potentials, Chapter 9 includes a thorough discussion of the isotropic harmonic oscillator using the shell model of the nucleus as an example. The isotropic oscillator also permits introduction the concept of accidental degeneracy. Because they are constituents of oscillator eigenfunctions, an attempt is made to decrypt the different conventions that are used for Laguerre polynomials and associated Laguerre polynomials. In our experience, this is a source of confusion to many students. Also contained in this chapter is an elaboration on the Morse potential in which three-dimensional