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Math Help - The Math behind Quantum Mechanics

  1. #1
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    The Math behind Quantum Mechanics

    Hi everyone, my name is Ali Khan and I will hopefully be applying to the University of Cambridge soon. I am in the first year of college (not sure what you call it in America, it's the stage of education attended by 16/17 year olds) and in order to prepare a strong University application, I am planning on studying some extra maths over the summer.

    My passion is particle physics and I understand the mathematical aspect of this science is called Quantum Mechanics.

    I would like to be able to understand aspects of Quantum Mechanics and be able to calculate, for example, wave equations within the next few months.

    It sounds ambitious but I'm passionate and a fast learner, although I do occasionally need clarification on certain topics

    My question is what aspects of mathematics do I need to learn and understand before I tackle quantum mechanics?

    I've heard differential equations are quite important in this field, what aspects of differential equations (and other math) do I need to study?

    Thanks,
    Ali Khan
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by AAKhan07 View Post
    Hi everyone, my name is Ali Khan and I will hopefully be applying to the University of Cambridge soon. I am in the first year of college (not sure what you call it in America, it's the stage of education attended by 16/17 year olds) and in order to prepare a strong University application, I am planning on studying some extra maths over the summer.

    My passion is particle physics and I understand the mathematical aspect of this science is called Quantum Mechanics.

    I would like to be able to understand aspects of Quantum Mechanics and be able to calculate, for example, wave equations within the next few months.

    It sounds ambitious but I'm passionate and a fast learner, although I do occasionally need clarification on certain topics

    My question is what aspects of mathematics do I need to learn and understand before I tackle quantum mechanics?

    I've heard differential equations are quite important in this field, what aspects of differential equations (and other math) do I need to study?

    Thanks,
    Ali Khan
    Calculus, calculus, calculus! As far as your school will let you. Then differential equations.

    Now, take it from a fellow Quantum Physicist, if you are serious about continuing in Particle or Quantum Physics you will want to take the following at some point (not necessarily for your BS):
    Linear Algebra (good idea before your BS)
    Group Theory
    Partial Differential Equations
    Your faculty will likely tell you (especially in your graduate program) that you will learn all the Math you need within the Physics program. I would beg to differ and suggest that you take them from the Math department (as well as any Physics classes that teach these as well.)

    -Dan
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  3. #3
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    Thanks

    Thanks for that Dan, I have noticed quite a lot of group theory while reading articles about quantum physics, notations such as su(3) relating to the strong force seem to have some sort of connection to group theory.

    I'll certainly read up on that, what are partial differentiatial equations? Is linear algebra stuff like matrices?

    Thanks,
    Ali
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  4. #4
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    Top Quark!

    Also, I just remembered that I'm planning to write a research paper on the search for the top quark over summer, I'm sure you're the person to ask about that so I was wondering, what websites/books are good to read for information on how the top quark was eventually found at fermilab?
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by AAKhan07 View Post
    Also, I just remembered that I'm planning to write a research paper on the search for the top quark over summer, I'm sure you're the person to ask about that so I was wondering, what websites/books are good to read for information on how the top quark was eventually found at fermilab?
    Try this. It looks decent.

    -Dan
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