Since the main purpose of the book was to demonstrate the philosophy and spirit behind the standard formulation of quantum mechanics, a thorough discussion of applications have taken a somewhat backseat. This was also done to keep the book accessible to a wide audience. Even outsiders interested to get a glimpse of quantum mechanics could get by with some minimal linear algebra provided in the book itself. Thus, technical and calculational details (which cannot be avoided if one were to discuss applications) had to be mostly avoided in the main text. However, in order that the book could still serve as an introductory text for a mainstream course, we make an exception in this chapter. Here we treat three of the mostwell known applications of quantum mechanics: Harmonic Oscillator, Angular Momentum and Hydrogen Atom. Both the analytical and the algebraic, ladder operator methods are demonstrated for solving the eigenvalue problems for the Harmonic oscillator and angular momentum. Topics involving technical calculations (e.g., calculations involving Hermite polynomials, spherical harmonics, etc.), modelling of real life systems (e.g., atomic polarizability) and spin have been relegated to the problem sets with elaborate hints and guidelines for working through them.
Since the main purpose of the book was to demonstrate the philosophy and spirit behind the standard formulation of quantum mechanics, a thorough discussion of applications have taken a somewhat backseat. This was also done to keep the book accessible to a wide audience. Even outsiders interested to get a glimpse of quantum mechanics could get by with some minimal linear algebra provided in the book itself. Thus, technical and calculational details (which cannot be avoided if one were to discuss applications) had to be mostly avoided in the main text. However, in order that the book could still serve as an introductory text for a mainstream course, we make an exception in this chapter. Here we treat three of the mostwell known applications of quantum mechanics: Harmonic Oscillator, Angular Momentum and Hydrogen Atom. Both the analytical and the algebraic, ladder operator methods are demonstrated for solving the eigenvalue problems for the Harmonic oscillator and angular momentum. Topics involving technical calculations (e.g., calculations involving Hermite polynomials, spherical harmonics, etc.), modelling of real life systems (e.g., atomic polarizability) and spin have been relegated to the problem sets with elaborate hints and guidelines for working through them.
The goal of Quantum Mechanics I, A Problem Text, is to enable students to solve problems appropriate to their first course in quantum mechanics. Significantly detailed solutions to traditionally posed problems dominate. Theory and rationale are addressed in prescript and postscript narratives and/or within the solved problems to guide students; and clarify vocabulary, symbology, and terminology. Applications of the postulates are presented initially using arguments from linear algebra appropriate to discrete systems with low-dimensional vectors and matrix operators, introducing orthogonality, orthonormality, Hermiticity, eigenvectors, eigenvalues, probability, expectation value, and degeneracy. These arguments blend into infinite-dimensional vectors and operators, and calculus-based arguments for continuous systems where delta functions, theta functions, and Fourier transforms are initially discussed. Dirac notation is fully developed within these first five chapters. Chapter six discusses Ehrenfest’s theorem, the Heisenberg uncertainty relations, and Gaussian wave functions and wave packets. Increasingly sophisticated potential energy functions are then treated to include the free particle, the infinite square well, the one-dimensional scattering state, the simple harmonic oscillator, the finite square well, orbital angular momentum, and the hydrogen atom. Ladder operators are featured in the developments of the simple harmonic oscillator and orbital angular momentum. The diversity of narratives and detailed solutions intend
The goal of Quantum Mechanics I, A Problem Text, is to enable students to solve problems appropriate to their first course in quantum mechanics. Significantly detailed solutions to traditionally posed problems dominate. Theory and rationale are addressed in prescript and postscript narratives and/or within the solved problems to guide students; and clarify vocabulary, symbology, and terminology. Applications of the postulates are presented initially using arguments from linear algebra appropriate to discrete systems with low-dimensional vectors and matrix operators, introducing orthogonality, orthonormality, Hermiticity, eigenvectors, eigenvalues, probability, expectation value, and degeneracy. These arguments blend into infinite-dimensional vectors and operators, and calculus-based arguments for continuous systems where delta functions, theta functions, and Fourier transforms are initially discussed. Dirac notation is fully developed within these first five chapters. Chapter six discusses Ehrenfest’s theorem, the Heisenberg uncertainty relations, and Gaussian wave functions and wave packets. Increasingly sophisticated potential energy functions are then treated to include the free particle, the infinite square well, the one-dimensional scattering state, the simple harmonic oscillator, the finite square well, orbital angular momentum, and the hydrogen atom. Ladder operators are featured in the developments of the simple harmonic oscillator and orbital angular momentum. The diversity of narratives and detailed solutions intend
The goal of Quantum Mechanics I, A Problem Text, is to enable students to solve problems appropriate to their first course in quantum mechanics. Significantly detailed solutions to traditionally posed problems dominate. Theory and rationale are addressed in prescript and postscript narratives and/or within the solved problems to guide students; and clarify vocabulary, symbology, and terminology. Applications of the postulates are presented initially using arguments from linear algebra appropriate to discrete systems with low-dimensional vectors and matrix operators, introducing orthogonality, orthonormality, Hermiticity, eigenvectors, eigenvalues, probability, expectation value, and degeneracy. These arguments blend into infinite-dimensional vectors and operators, and calculus-based arguments for continuous systems where delta functions, theta functions, and Fourier transforms are initially discussed. Dirac notation is fully developed within these first five chapters. Chapter six discusses Ehrenfest’s theorem, the Heisenberg uncertainty relations, and Gaussian wave functions and wave packets. Increasingly sophisticated potential energy functions are then treated to include the free particle, the infinite square well, the one-dimensional scattering state, the simple harmonic oscillator, the finite square well, orbital angular momentum, and the hydrogen atom. Ladder operators are featured in the developments of the simple harmonic oscillator and orbital angular momentum. The diversity of narratives and detailed solutions intend
The goal of Quantum Mechanics I, A Problem Text, is to enable students to solve problems appropriate to their first course in quantum mechanics. Significantly detailed solutions to traditionally posed problems dominate. Theory and rationale are addressed in prescript and postscript narratives and/or within the solved problems to guide students; and clarify vocabulary, symbology, and terminology. Applications of the postulates are presented initially using arguments from linear algebra appropriate to discrete systems with low-dimensional vectors and matrix operators, introducing orthogonality, orthonormality, Hermiticity, eigenvectors, eigenvalues, probability, expectation value, and degeneracy. These arguments blend into infinite-dimensional vectors and operators, and calculus-based arguments for continuous systems where delta functions, theta functions, and Fourier transforms are initially discussed. Dirac notation is fully developed within these first five chapters. Chapter six discusses Ehrenfest’s theorem, the Heisenberg uncertainty relations, and Gaussian wave functions and wave packets. Increasingly sophisticated potential energy functions are then treated to include the free particle, the infinite square well, the one-dimensional scattering state, the simple harmonic oscillator, the finite square well, orbital angular momentum, and the hydrogen atom. Ladder operators are featured in the developments of the simple harmonic oscillator and orbital angular momentum. The diversity of narratives and detailed solutions intend
Many students find quantum mechanics conceptually difficult when they first encounter the subject. In this book, the postulates and key applications of quantum mechanics are well illustrated by means of a carefully chosen set of problems, complete with detailed, step-by-step solutions. Beginning with a chapter on orders of magnitude, a variety of topics are then covered, including the mathematical foundations of quantum mechanics, Schrödinger's equation, angular momentum, the hydrogen atom, the harmonic oscillator, spin, time-independent and time-dependent perturbation theory, the variational method, multielectron atoms, transitions and scattering. Throughout, the physical interpretation or application of certain results is highlighted, thereby providing useful insights into a wide range of systems and phenomena. This approach will make the book invaluable to anyone taking an undergraduate course in quantum mechanics.
The goal of Quantum Mechanics I, A Problem Text, is to enable students to solve problems appropriate to their first course in quantum mechanics. Significantly detailed solutions to traditionally posed problems dominate. Theory and rationale are addressed in prescript and postscript narratives and/or within the solved problems to guide students; and clarify vocabulary, symbology, and terminology. Applications of the postulates are presented initially using arguments from linear algebra appropriate to discrete systems with low-dimensional vectors and matrix operators, introducing orthogonality, orthonormality, Hermiticity, eigenvectors, eigenvalues, probability, expectation value, and degeneracy. These arguments blend into infinite-dimensional vectors and operators, and calculus-based arguments for continuous systems where delta functions, theta functions, and Fourier transforms are initially discussed. Dirac notation is fully developed within these first five chapters. Chapter six discusses Ehrenfest’s theorem, the Heisenberg uncertainty relations, and Gaussian wave functions and wave packets. Increasingly sophisticated potential energy functions are then treated to include the free particle, the infinite square well, the one-dimensional scattering state, the simple harmonic oscillator, the finite square well, orbital angular momentum, and the hydrogen atom. Ladder operators are featured in the developments of the simple harmonic oscillator and orbital angular momentum. The diversity of narratives and detailed solutions intend