Lecture12 - Postulates of quantum mechanics Any state of a...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Physical Chemistry Lecture 12 Wave Equations and States Postulates of quantum mechanics Any state of a dynamical system of N particles is described as fully as is possible by a function, , such that the quantity * d 3 r is proportional to the probability of finding r between r and r + d 3 r . For every observable property of a system, there exists a corresponding linear hermitian operator The physical properties of the observable can be inferred from the mathematical properties of its associated operator. The measurement of a physical observable gives only one of the eigenvalues corresponding to that observable. Origins of quantum mechanics Hamilton’s equation for the energy of a classical system Schroedinger’s equation for the wave function of a system with a definite energy Where is the wave function corresponding to the energy E H E H ˆ Expectation value of a property If a system is in a state with wave function, , the measured property is given by an integral Must know botb the state and the operator to find the value Expectation values of measurables are real Requirement on the wave function and operator The operator must be a hermitian operator space all dV O O ˆ * space all space all dV O dV O * * ˆ ˆ Choosing operators Operators for various observables are found by correspondence to classical equivalents For position, the operation is
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern