Cat in the box
I walked into the lecture theatre and took my seat. The lecturer tapped a dusty blackboard and began.
"Carrying on from last time, in the mathematical formulation of quantum mechanics each system is associated with a complex Hilbert space such that each instantaneous state of the system is described by a unit vector in that space. This state vector encodes the probabilities for the outcomes of all possible measurements applied to the system. As the state of a system generally changes over time, the state vector is a function of time. The Schrödinger equation provides a quantitative description of the rate of change of the state vector. The Schrödinger equation is written aitch tee brackets psi ecks comma tee brackets equals eye aitch bar delta over delta tee psi ecks tee brackets, where eye is the unit imaginary number, aitch bar is Planck's constant divided by two pi and the Hamiltonian aitch tee is a self-adjoint operator acting on the state space. In non-relativistic quantum mechanics, the Hamiltonian of a particle can be expressed as the sum of two operators, one corresponding to kinetic energy and the other to potential energy. For a single particle of mass em with no electric charge and no spin, the kinetic energy operator is tee equals pee squared over two em, where pee is the momentum operator, which is defined as pee psi are comma tee brackets equals aitch bar over eye invert triangle psi are comma tee brackets. The potential energy operator is vee equals vee are brackets, where vee is a real scalar function of the position operator are. Putting these together we obtain aitch psi are comma tee brackets equals tee plus vee brackets psi are comma tee brackets equals square bracket minus aitch bar squared over two em invert triangle squared plus vee are brackets square bracket psi are comma tee brackets equals eye aitch bar delta psi over delta tee are comma tee brackets, where invert triangle squared is the Laplace operator. This is a commonly encountered form of the Schrödinger wave equation, though not the most general one. Does anyone have any questions at this point?"
I raised my hand.
"Is this British And European History From 1650 To 1850?" I asked.
"No," he said.
So I left.
"Carrying on from last time, in the mathematical formulation of quantum mechanics each system is associated with a complex Hilbert space such that each instantaneous state of the system is described by a unit vector in that space. This state vector encodes the probabilities for the outcomes of all possible measurements applied to the system. As the state of a system generally changes over time, the state vector is a function of time. The Schrödinger equation provides a quantitative description of the rate of change of the state vector. The Schrödinger equation is written aitch tee brackets psi ecks comma tee brackets equals eye aitch bar delta over delta tee psi ecks tee brackets, where eye is the unit imaginary number, aitch bar is Planck's constant divided by two pi and the Hamiltonian aitch tee is a self-adjoint operator acting on the state space. In non-relativistic quantum mechanics, the Hamiltonian of a particle can be expressed as the sum of two operators, one corresponding to kinetic energy and the other to potential energy. For a single particle of mass em with no electric charge and no spin, the kinetic energy operator is tee equals pee squared over two em, where pee is the momentum operator, which is defined as pee psi are comma tee brackets equals aitch bar over eye invert triangle psi are comma tee brackets. The potential energy operator is vee equals vee are brackets, where vee is a real scalar function of the position operator are. Putting these together we obtain aitch psi are comma tee brackets equals tee plus vee brackets psi are comma tee brackets equals square bracket minus aitch bar squared over two em invert triangle squared plus vee are brackets square bracket psi are comma tee brackets equals eye aitch bar delta psi over delta tee are comma tee brackets, where invert triangle squared is the Laplace operator. This is a commonly encountered form of the Schrödinger wave equation, though not the most general one. Does anyone have any questions at this point?"
I raised my hand.
"Is this British And European History From 1650 To 1850?" I asked.
"No," he said.
So I left.
posted by Ecks Ridgehead at
1/11/2006 08:30:00 am
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