Midterm1 - Name February 26, 2010 Chemistry 120A Hour...

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

View Full Document Right Arrow Icon
February 26, 2010 Chemistry 120A Hour Examination Useful formulas Schr¨ odinger’s time-dependent equation in one dimension: i ~ Ψ( x,t ) /∂t = H Ψ( x,t ) , where ~ is Planck’s constant over 2 π , H is the Hamiltonian operator, and Ψ( x,t ) is the wave-function as a function of position, x , and time, t . The Hamiltonian for a particle of mass m in d = 1 is H = 1 2 m ˆ p 2 + V ( x ) = - ~ 2 2 m d 2 dx 2 + V ( x ) , where ˆ p = momentum operator, and V ( x ) = potential energy. Stationary solutions to Schr¨ odinger’s equation are of the form Ψ stationary ( x,t ) = ψ ( x ) e - iEt/ ~ , where ψ ( x ) is the solution to the eigenvalue equation H ψ ( x ) = E ψ ( x ) . The momentum operator , ˆ p = ( ~ /i ) d/dx , obeys x ˆ p - ˆ px [ x, ˆ p ] = i ~ Time derivative of expectation value for a general observable G is d dt Z h Ψ * ( x,t ) ˆ G Ψ( x,t ) i dx = d h ˆ G i /dt = (1 /i ~ ) h [ ˆ G, H ] i . 1
Background image of page 1

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

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

Page1 / 4

Midterm1 - Name February 26, 2010 Chemistry 120A Hour...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online