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Tag Archives: Schrödinger Equation

Last time I began exploring the similarity between the **Schrödinger equation** and a classical **heat diffusion equation**. In both cases, valid solutions push the *high curvature* parts of their respective functions towards flatness. The effect is generally an averaging out in whatever space the function occupies.

Both equations involve *partial* derivatives, and I ignored that in our simple one-dimensional case. Regular derivatives were sufficient. But math in two dimensions, let alone in three, requires partial derivatives.

Which were yet another hill I faced trying to understand physics math. If they are as opaque to you as they were to me, read on…

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10 Comments | tags: derivatives, exponential function, partial derivatives, QM101, Schrödinger Equation | posted in Math, Physics

This is the first of a series of posts exploring the mysterious Schrödinger Equation — a central player of quantum mechanics. Previous QM-101 posts have covered important foundational topics. Now it’s time to begin exploring that infamous, and perhaps intimidating, equation.

We’ll start with something similar, a classical equation that, among other things, governs how heat diffuses through a material. For simplicity, we’ll first consider a one-dimensional example — a thin metal rod. (Not truly one-dimensional, but reasonably close.)

Traveller’s Advisory: Math and graphs ahead!

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8 Comments | tags: derivatives, exponential function, QM101, quantum, Schrödinger Equation | posted in Math, Physics

The previous post began an exploration of a key conundrum in quantum physics, **the question of measurement** and the deeper mystery of the divide between **quantum** and **classical** mechanics. This post continues the journey, so if you missed that post, you should go read it now.

Last time, I introduced the notion that “measurement” of a quantum system causes “wavefunction collapse”. In this post I’ll dig more deeply into what that is and why it’s perceived as so disturbing to the theory.

*Caveat lector*: This post contains a tiny bit of simple geometry.

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10 Comments | tags: measurement problem, QM101, quantum mechanics, quantum physics, Schrödinger Equation | posted in Opinion, Physics

I’m two-thirds through my second **Paul Halpern** book this month. Earlier I read his book about cosmology, *Edge of the Universe: A Voyage to the Cosmic Horizon and Beyond* (2012), which was okay. Now I’m reading *The Quantum Labyrinth: How Richard Feynman and John Wheeler Revolutionized Time and Reality* (2017), which I’m enjoying a bit more. In part because cosmology has changed more since 2012 than quantum physics has since 2017. (Arguably, the latter hasn’t changed much since the 1960s.)

I wrote about Halpern’s book, *Einstein’s Dice and Schrödinger’s Cat* (2015), last year. As the title implies, it focuses on two great names from physics. *Quantum Labyrinth* (as its title also implies) also focuses on two great physics names.

But today’s Brain Bubble (as the title implies) is about **wavefunction collapse**.

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10 Comments | tags: Paul Halpern, quantum mechanics, Schrödinger Equation, wave-function | posted in Brain Bubble, Physics

This is the third part of a series examining the **Many Worlds Interpretation** of Quantum Mechanics (the **MWI** of QM). The popularity of the MWI in books, blogs, and science videos, especially among the science-minded, tends to keep in present in some corner of my mind. Blog posts are a way to shoo it out.

The first part introduced the topic and talked about cats. The second part discussed the Schrödinger equation, wavefunctions, decoherence, and the question of how multiple instances of matter can coincide. That question, to me, is a central issue I have with MWI.

This time I dig into **quantum superposition** and touch on a few other topics.

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14 Comments | tags: Many Worlds Interpretation, MWI, Schrödinger Equation, wave-function | posted in Physics

Last time I started exploring questions I have about the **Many Worlds Interpretation** of Quantum Mechanics (the MWI of QM). Obviously I’m not a fan; quite the opposite. It presents as parsimonious, hung on the single hook of a universal wavefunction, but I think it gets more complicated and cumbersome when examined. I can’t say it’s *broken*, but I don’t find it very attractive.

I suspect most people, even in physics, don’t care. A few have invested themselves in books or papers, but these interpretations don’t matter to real physics work. The math is the math. But among the philosophical, especially the ontological, it’s food for debate.

Being both philosophical and ontological, I do smell what’s cooking!

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13 Comments | tags: Many Worlds Interpretation, MWI, Schrödinger Equation, wave-function | posted in Physics

Remember when “going viral” didn’t mean hospitalization and possible death? (Obviously if we go back even further to the original meaning, it did.) I had an old post go briefly and mildly viral last week. Big traffic spike with a very rapid tail-off. Most bemusing.

I’ll tell you about that, and about a spike on another post, this one weirdly seasonal — huge spike ever September for three years now. I have no idea what’s going on there. Most puzzling.

There is also a book about the friendship and conflict between **Albert Einstein** and **Erwin Schrödinger** that I thoroughly enjoyed despite it not being my typical sort of reading (I’ve never gone in much for either history or biography).

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3 Comments | tags: Albert Einstein, blog, blogging, Einstein's Dice, Erwin Schrödinger, General Relativity, Leon Wieseltier, Paul Halpern, Schrödinger Equation, Schrödinger's Cat, Special Relativity | posted in Books

Last time I started with wave-functions of quantum systems and the **Schrödinger equation** that describes them. The wave-like nature of quantum systems allows them to be merged (superposed) into combined quantum system so long as the coherence (the phase information) remains intact.

The big mystery of quantum wave-functions involves their apparent “collapse” when an interaction with (a “measurement” by) another system seemingly destroys their coherence and, thus, any superposed states. When this happens, the quantum behavior of the system is lost.

This time I’d like to explore what I think might be going on here.

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16 Comments | tags: quantum effects, quantum mechanics, quantum physics, Schrödinger Equation, wave-function | posted in Physics

**Quantum physics** is weird. How weird? *“Too weird for words,”* as we used to say, and there is a literal truth to words being inadequate in this case. There is no way to look at the quantum world that doesn’t break one’s mind a little. No one truly *understands* it (other than through the math). It’s like trying to see inside your own head.

Since we’re clueless we make up stories to fit the facts. Some stories advise that we just keep our heads down and do the math. (Which works very well but leaves us thirsty.) Other stories seek to quench that thirst, but every story seems to stumble somewhere.

One of quantum’s biggest and oldest stumbling blocks is *wave-function collapse*.

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17 Comments | tags: quantum effects, quantum mechanics, quantum physics, Schrödinger Equation, wave-function | posted in Physics

I was surprised to discover I’ve never posted about the **Many Worlds Interpretation** (**MWI**) of quantum physics — I would have sworn I had. I’ve *mentioned* it a few times, and I know I’ve discussed it in comment sections, but it seems I never tackled the subject explicitly for the record.

It’s been on my mind lately because others have talked about it. Sean Carroll’s book promoting it generated a wave of discussion. The final push for me was Jim Baggott’s *Farewell to Reality*, which consigns MWI to the “fairy tale physics” heap.

Since I quite agree, this seems a good followup to yesterday’s post.

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11 Comments | tags: Copenhagen Interpretation, Many Worlds Interpretation, measurement problem, MWI, Schrödinger Equation, Schrödinger's Cat | posted in Philosophy, Physics