Mathematics of Quantum Mechanics

In summary, the individual is seeking guidance on learning the mathematics of Quantum Physics without taking academic courses. They have a strong interest in Astronomy and Quantum Physics but ended up becoming a Business Consultant. They have a basic understanding of the theories but lack mathematical understanding. They are looking for recommendations of books or websites to guide them through the basic to advanced mathematics of Quantum Physics. The Theoretical Minimum is a highly recommended resource for this purpose.
  • #1
Agreegate
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I have a question about learning the mathematics of Quantum Physics...

So, I've been really interested in Astronomy and Quantum Physics since I was a kid. Owing to some accidental education and career choices, I however, ended up becoming a Business Consultant. Although I have spend most of my life reading about and learning about Quantum Mechanics, Physics and Astronomy, but now, I have reached a point where I understand most of the theories in principle, but lack any understanding of how they work mathematically... It feels synonymous to being an illiterate person who has to rely on what others read to him from a storybook, but cannot read it himself.

My basic mathematics knowledge is set very very far back at this point. I hardly remember high school mathematics, but can probably recall it again with some effort and learn more on top of it. What I need, is a guidance on what kind of mathematics I should invest my time in learning, so that I can work towards mathematically understanding Quantum Physics (no academic courses, I want to learn it in my own time, myself, since, I'm not aiming for an academic or professional career). Also, if someone can recommend a book or website, etc, which can guide me through basic to advanced mathematics of Quantum Physics, then that would be brilliant. Thanks for your help in advance...
 
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  • #3
Agreegate said:
I have a question about learning the mathematics of Quantum Physics...

So, I've been really interested in Astronomy and Quantum Physics since I was a kid. Owing to some accidental education and career choices, I however, ended up becoming a Business Consultant. Although I have spend most of my life reading about and learning about Quantum Mechanics, Physics and Astronomy, but now, I have reached a point where I understand most of the theories in principle, but lack any understanding of how they work mathematically... It feels synonymous to being an illiterate person who has to rely on what others read to him from a storybook, but cannot read it himself.

My basic mathematics knowledge is set very very far back at this point. I hardly remember high school mathematics, but can probably recall it again with some effort and learn more on top of it. What I need, is a guidance on what kind of mathematics I should invest my time in learning, so that I can work towards mathematically understanding Quantum Physics (no academic courses, I want to learn it in my own time, myself, since, I'm not aiming for an academic or professional career). Also, if someone can recommend a book or website, etc, which can guide me through basic to advanced mathematics of Quantum Physics, then that would be brilliant. Thanks for your help in advance...
I hear good things about The Theoretical Minimum.
https://www.amazon.com/dp/0465075681/?tag=pfamazon01-20
 
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1. What is the significance of complex numbers in quantum mechanics?

The use of complex numbers in quantum mechanics allows for the representation of complex wave functions, which are essential in describing the probabilistic nature of quantum systems. Complex numbers also help to explain the phenomenon of quantum entanglement and the concept of superposition.

2. How does the uncertainty principle relate to the mathematics of quantum mechanics?

The uncertainty principle, first proposed by Werner Heisenberg, is a fundamental principle in quantum mechanics that states that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa. This principle is mathematically represented by the commutator of two operators, such as position and momentum.

3. Can the mathematics of quantum mechanics be used to predict the exact outcome of a measurement?

No, the mathematics of quantum mechanics can only predict the probability of a particular outcome. This is due to the probabilistic nature of quantum systems, where the state of a particle is described by a wave function that contains all possible outcomes with varying probabilities.

4. What is the role of operators in the mathematics of quantum mechanics?

Operators in quantum mechanics represent physical observables, such as position, momentum, and energy. They act on the wave function to extract information about the system. The eigenvalues of these operators correspond to the possible outcomes of a measurement, and the corresponding eigenvectors represent the state of the system after the measurement.

5. How does the mathematics of quantum mechanics differ from classical mechanics?

Classical mechanics is based on deterministic equations that can accurately predict the behavior of macroscopic objects. In contrast, quantum mechanics is based on probabilistic equations that can only predict the likelihood of outcomes for microscopic objects. Additionally, classical mechanics operates in a continuous space, while quantum mechanics operates in a discrete space. The two theories are fundamentally different and cannot be reconciled.

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