{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture15 - CHEM 356 Lecture 15 Fall 2009 1 Barrier...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
CHEM 356, Lecture 15, Fall 2009 1 Barrier Potentials. Classical Mechanics: a particle of energy ? in region I and incident upon the barrier in the + 𝑥 –direction will have probability unity of being reflected if ? < 𝑉 0 , and probability unity of being transmitted if ? > 𝑉 0 . Quantum Mechanics: neither statement holds. Schr¨ odinger equation: Regions I, III: 𝑑 2 𝜓 𝑑𝑥 2 = 𝑘 2 1 𝜓 ; 𝑘 1 = 2 𝑚? , and 𝜓 I ( 𝑥 ) = ? e 𝑖𝑘 1 𝑥 + ? e 𝑖𝑘 1 𝑥 , 𝑥 < 0 , 𝜓 III ( 𝑥 ) = ? e 𝑖𝑘 1 𝑥 + ? e 𝑖𝑘 1 𝑥 , 𝑥 > 𝑎 . Region II: 𝑑 2 𝜓 II 𝑑𝑥 2 = 2 𝑚 ( 𝑉 0 ? ) 2 𝜓 II
Background image of page 1

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

View Full Document Right Arrow Icon
CHEM 356, Lecture 15, Fall 2009 2 The form of the solution in region II depends upon whether ? < 𝑉 0 or ? > 𝑉 0 : ? < 𝑉 0 𝜓 II ( 𝑥 ) = ? e 𝑘 2 𝑥 + ? e 𝑘 2 𝑥 ; 0 𝑥 𝑎 ; 𝑘 2 = 2 𝑚 ( 𝑉 0 ? ) ? > 𝑉 0 𝜓 II ( 𝑥 ) = ? e 𝑖𝑘 2 𝑥 + ? e 𝑖𝑘 2 𝑥 ; 0 𝑥 𝑎 ; 𝑘 2 = 2 𝑚 ( ? 𝑉 0 ) Physically: in region III, we may set ? = 0, as there can be only a transmitted wave.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}