Chapter5_8 - t and ∆ k represents an uncertainty in the...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
PHY3063 R. D. Field Department of Physics Chapter5_8.doc University of Florida Inescapable Consequence of Wave Packets De Broglie postulated that the “pilot wave- packet” governs the motion of the electron. However, the electron is a “point like” elementary particle ( i.e. radius zero! ). So where exactly is the electron within the pilot wave-packet? The electron moves with speed v group somewhere within the pilot wave packet given by ( ) ( ) t kx t x P t kx t x k t x ω ω ω = Ψ sin ) , ( sin 2 2 cos 2 ) , ( . The term P(x,t) describes the “wave-packet”. As a crude guess lets say that at fixed time t the electron must be somewhere in the region x = x n+1 - x n , where the position of the n th node ( i.e. zeros) of the wave-packet is given by π ω ) 1 2 ( + = n t kx n . Thus at fixed time t , k k t n t n x x x n n = + + + + = + π ω π ω π 2 ) 1 2 ( ) 1 ) 1 ( 2 ( 1 and hence π 2 k x . Here x represents an uncertainty in the electrons position at time
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: t and ∆ k represents an uncertainty in the electrons precise wave number. Due to the nature of wave superposition asking for a small uncertainty in the position ∆ x of the electron requires a larger ∆ k and hence a bigger uncertainty in the electrons wave number. Similarly at fixed position x , 2 ≈ ∆ ∆ t . Here ∆ t represents an uncertainty in the time and ∆ω represents an uncertainty in the electrons angular frequency. Again due to the nature of wave superposition asking for a small uncertainty in the time ∆ t requires a larger ∆ω and hence a bigger uncertainty in the electrons angular frequency. Wave Packet-3-2-1 1 2 3 x v group electron v group ∆ x Wave Packet-3-2-1 1 2 3 t electron ∆ t At fixed time t At fixed x Wave of what?...
View Full 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