{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chapter6_1 - Quantum Mechanics Give up the idea of...

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 Chapter6_1.doc University of Florida How Do We Interpret Pilot Waves? Probabilistic Interpretation: In 1926 Max Born suggested that we interpret the “pilot waves” as “probability amplitudes” called “wave functions” where ) , ( t r r Ψ = “probability amplitude” and 2 ) , ( ) , ( t r t r r r Ψ = ρ = “probability density” such that r d t r 3 ) , ( r ρ is the probability of finding the particle at time t within the small region d 3 r = dxdydz about the point r r . Must require that the overall probability of finding the particle somewhere be finite: finite N r d t r r d t r allSpace allSpace = = Ψ = 3 2 3 ) , ( ) , ( r r ρ Now normalize the probability of finding the particle somewhere in space to one: 1 ) , ( 3 2 = Ψ allSpace N r d t r r , where N t r t r N / ) , ( ) , ( r r Ψ = Ψ . However, must require that Ψ (x,y,z,t) be a “square integrable” function for all values of t. Note that the probability amplitude is a complex function , but the probability density is a real number and Probability = |probability amplitude|
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Quantum Mechanics: Give up the idea of predicting the result of a single measurement! Can determine only the probability of each of the many possible outcomes. Knowing the probabilities allows one to calculate average quantities and standard deviations. Rolling the Dice: It is like rolling a dice. You know there is a one in six chance of rolling a one, so that if you roll the dice millions of times then, on the average, the value one will occur 1/6 of the time. However, on a given roll you do not know which of the six numbers will appear. Gauge Invariance: Note that the following two wave functions describe the same state: ) , ( ) , ( 1 t r t r r r Ψ = Ψ and ) , ( ) , ( 2 t r e t r i r r Ψ = Ψ φ . Wave Packet-3-2-1 1 2 3 x v group At fixed time t Probability amplitude! Many amplitudes correspond to the same probability! Also require Ψ to be continuous and single-valued!...
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