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    Mix mathematics with physics in undergrad degree?

    As far as I know, it just means there are more mandatory upper-level classes because you have to meet the minimum requirements for two degrees instead of one. It's typically somewhat easier with related subjects like math and physics because the introductory courses overlap. My advisor's...
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    Do entry level PhD statisticians really make 200K a year?

    I've never heard of anyone making $200K immediately after getting a statistics PhD. If it happens, I'd bet it's a rare outlier like D H said. There are definitely $100K+ positions for recent statistics PhDs. For PhDs with no industry experience, I think the key to a higher salary is to find...
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    Question regarding the crazy road to a PhD

    From personal and anecdotal experience, I'd guess that 10% of academics will think it's cool that you have an outside perspective 20% will feel threatened and try to sabotage you by telling people you're too dumb for academia 30% will think it's irrelevant how you got your degree as long as you...
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    Change of variables in conditional pdf

    Is ##t## random? From the description of the problem, I get the impression that it's a deterministic parameter. If I understand correctly, the key part of the problem is this: You know the pdf (probability density function) of each ##r_t## You want to know the pdf of the product of many...
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    Mix mathematics with physics in undergrad degree?

    I got a math undergrad and a physics PhD. My advisor double-majored in math/physics as an undergrad, then got a physics PhD, then wrote several math and physics textbooks. So it's definitely possible to mix-and-match. There's often some catch-up work you'll need to do if you major in one and...
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    Do you have any interest in Quaternionic Quantum Mechanics?

    It's possible to represent any qubit observable as a quaternion and any pure qubit state as a unit quaternion. Single-qubit QM can be written entirely in terms of quaternions without reference to state vectors, density matrices, or operators. I discovered this by accident working on my...
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    Will the Sputnik generation retire in time?

    I don't personally know of anything that extreme, but a lesser version is happening right now. Government cuts started a chain reaction which led to people at the bottom of the pecking order (grad students with no grant money) being forced out of the program or rushed to graduate early.
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    Programs Physics? Without a degree?

    I think it would be very, very improbable, mostly because: That's the situation right now in the US and Canada. (Maybe there are exceptions in Europe, Japan, or Australia - I don't really know.) I still think it's possible for a skilled person with no PhD to do physics, just not to be a...
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    Wave Function Collapse and Entropy

    Since we're throwing around lots of interpretations of entropy, I can't resist adding my personal favorites as fuel to the fire: E. T. Jaynes argued that "entropy of a system" is an ill-defined concept. Entropy should be defined for probability distributions, not for physical systems. In...
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    Physics Job Opportunities

    I have no personal experience with this question, and many people on PhysicsForums say the answer is "no." But I know at least 2 people who were hired as engineers immediately after they finished a physics undergraduate degree, so it must not be too improbable. Both were hired by large US...
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    How to get started with quantum mechanics?

    If you really want to get past pop-sci and heuristic arguments, spend some time learning linear algebra fundamentals. It's essential to know what these words mean: vector space inner product linear combination / superposition linear transformation orthogonal, normal, orthonormal...
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    Physics problems related to green function ?

    The Schrödinger equation* is a linear PDE with a ##\nabla^2## in it: ## \imath \hbar \partial_t \Psi(\mathbf{r},t) = \frac{-\hbar^2}{2m}\nabla^2 \Psi(\mathbf{r},t) + V(\mathbf{r},t) \Psi(\mathbf{r},t) ## So it can be useful in QM to know Green's functions for the Helmholtz equation...
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    Very simple question, believe teacher is wrong.

    Could there have been a miscommunication or misunderstanding of the problem? If not, then your answer (and Dickfore's) is correct. The teacher's answer is the probability that 3 out of 3 randomly-selected tires are faulty. I'm assuming the failure probability for each tire is independent of...
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    Informative Reality Check

    This is definitely true. Your age is not a problem unless the admissions committee has some unusually irrational prejudices. It might even be an advantage in some ways. Assuming you're planning to study in the United States, the usual problems still apply: student debt, low pay, and uncertain...
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    MTech fresher in electronics domain

    I had never heard of them either, and looking them up gave me an excuse to procrastinate an extra few minutes. I think IISC, IITS, NITs are universities, Wipro is a consulting firm, and all are based in India. I'm fairly confident that almost nobody in Europe or North America would recognize...
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    Exponential of Gaussian Distribution

    What mathman said is right - I just wanted to add a couple of things: 1) The Law of the Unconscious Statistician is a snarky name for the usual way to find the EV of a function of a random variable. ## E[y(X)] = \int y(x) f_X(x) dx ## ## E[e^{jX}] = \frac{1}{\sigma\sqrt{2\pi}} \int e^{jx}...
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    Invariant Matrix norm

    By change of basis, I assume you mean changing from one orthonormal basis to another orthonormal basis. If so, then I think any matrix norm which is compatible with the norm you're using for vectors will be the same in either basis. An important example is the spectral norm. This norm is...
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    What's the difference between Bell curve and Gaussian distribution

    Often bell curve and Gaussian distribution are used interchangeably with normal distribution. But sometimes people use bell curve to mean anything which looks kind of like a bell: smooth, with one lump in the middle, two inflection points, and rapidly-decreasing tails on either end. I usually...
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    Career choice!

    What I wish people had told me when I was 18: the option to choose your career is a rare privilege. Quite a bit of my career "choices" were made for me by economic factors and random luck. But you don't have to be completely helpless - you can exert some influence over your options. My...
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    Did I mess up by not choosing a famous advisor?

    Agreed! There's a scary amount of random variance in PhD outcomes. Many of the most important variables are things like: Is your advisor a narcissist? Will your advisor move and/or get fired in the next 6 years? Will your advisor be interested in the topic you will be interested in 1-6...
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    Random walk or binomial?

    Your method works fine, except I think part b) is answering the wrong question. If the drunk ever gets to +6, then he goes inside and stops walking. I think your answer to b) is the number of paths which end at +6. This neglects any paths which get to +6 at some time ##t<20##, but then end up...
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    The product rule and Bayes rule

    That looks right to me. In practice, conditional probability can become really confusing, especially when ##A## and ##B## are uncountable and ##P## is some kind of integral. But the main ideas follow from the set-theory argument you wrote. (Also, it only works if ##P(B)\neq0##, otherwise we just...
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    How to prepare for my first programming interview?

    I recently had a phone interview with a programmer. It must have gone fairly well because they invited me to visit for an in-person interview. The strategy I used was essentially: Don't panic. If you don't know something, admit it. If the interviewer gives you time to figure it out, try to...
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    About career path to Phd, Professor

    I'm in a US physics PhD program, and I agree with everything eri said. Agreed again, with a footnote: while you're doing PhD research, you can also learn things which many employers do care about. For example, I've used NumPy, Bayesian inference, and autocorrelation of time series in recent...
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    Physics Employment prospects of a physicist

    According to this article, NSF survey data suggests about 600 will work at a postdoc, 450 will work in private industry, and 450 will be unemployed. That's for all physical science PhDs, not just physics. The survey is taken at graduation, so it doesn't count people who only received job offers...
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    Question about a missed interview

    I had a similar situation recently. I was scheduled for an interview but never received a call. I emailed the HR person who was responsible for scheduling my interview. Apparently he/she gave the wrong phone number to the interviewer. So I gave them my correct number again. (I listed it...
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    Hamiltonian eigenstate problem

    When ##t \neq t'##, ##\hat{H}## is ##\tfrac{1}{2}\hbar \omega_0## times the identity matrix. Then every vector is an eigenvector with eigenvalue ##\tfrac{1}{2}\hbar \omega_0##. When ##t = t'##, ##\hat{H}## is ## \hat{H} = \frac{\hbar}{2} \begin{bmatrix} \omega_0 & \infty \\ \infty &...
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    Hamiltonian eigenstate problem

    I'm confused: are those ##\delta##'s Dirac delta functions? If so, then ##\hat{H}(t)## is ill-defined when ##t=t'##. (The integral ##\int \hat{H}(t) dt## can still be defined using step functions.) I think there might be a typo in there, too. The usual way to write ##\hat{H}## for a spin-1/2 in...
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    Pdf of angle formed by two normal random variables

    Thanks for the link - this is a pretty cool-looking paper! I recognize the name, too: Marsaglia invented the polar method for generating pairs of standard normal pseudorandom numbers. It might be easier to represent the random point (X,Y) in polar coordinates (R,θ). I'd start by first...
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    Teaching Different Physics Courses

    Here's a possible starting point for your reply: the students' backgrounds will be very different for those classes. How will you adapt your lesson plans and/or teaching style to adjust? For example, 'conceptual physics' is usually designed for people who want a general overview rather than...
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