Schrodingers Equation in 3 space Dimension

In summary, a "vector of x = x,y,z" is a vector that has three components (x, y, z), and a given vector will have projections on x, y, and z axes.
  • #1
hell18
21
0
i read a book on quantium theory, it states that a vector of x = x,y,z. When i think about 3 dimensional space, we cannot see that, is that correct?
 
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  • #2
We live in 3d space, addition of a time coordinate makes it 4d.

I am not sure what you are asking.
 
  • #3
A large part of our confusion is "vector of x = x,y,z". What do YOU mean by a "vector of x"?

Certainly it is true that a "position vector" must have 3 components: typically labeled x, y, z: that's what "3 dimensional" MEANS. It would not be very good practice to give a vector the same name as one of its components!
 
  • #4
Maybe he meant to bold the x for the vector? Still not goood usage, since one expects x = (x1,x2,x3).
 
  • #5
i thought a vector was a small section of the whole. but i don't think that is the case. In the book it says a 3 dimensional space vector of x = x,y,z. So space is 3d? so time is a 1 dimensional element? add those together get 4d? but i thought we cannot see the 4th dimension? or am i missing something out?
 
  • #6
I think you need to go back and study some precalculus. You need to spec up on some geometric concepts before tackling the Schroedinger equation.

A vector has two qualities, magnitude and direction. (Bear with me vector space fans, sufficient unto the day is the rigor thereof). For example a force has its magnitude (so many Newtons) and the direction in which it is applied. If you set up coordinates with an origin, any point is determined by a vector whose magnitude is the distance from the origin and whose direction is the direction from the origin to the point. This particular vector is called the radius vector.

Vectors have components. If you set up x y and z axes at right angles to each other, then a given radius vector will have projections on those axes and the length of the projections will give the components. So if the vector v has compnents a, b, and c we write v = (a,b,c).

This works for three dimensions, but relativity requires four, and that is another story entirely. Don't worry about it yet; the Schroedinger equation at the beginning level is not relativistic.
 

1. What is Schrodingers Equation in 3 space Dimension?

Schrodingers Equation in 3 space Dimension is a mathematical equation that describes the quantum behavior of a single particle in three-dimensional space. It was first proposed by Erwin Schrodingers in 1926 and is a fundamental equation in quantum mechanics.

2. What does the equation represent?

The equation represents the wave function of a particle in three-dimensional space. This wave function contains all the information about the possible states of the particle, including its position, momentum, and energy.

3. How is the equation used in quantum mechanics?

The equation is used to calculate the probability of finding a particle in a certain location or state. It is also used to predict the behavior of particles in quantum systems and to understand the properties of matter at the atomic and subatomic level.

4. Are there any limitations to this equation?

While Schrodingers Equation in 3 space Dimension is a powerful tool in quantum mechanics, it does have limitations. It cannot accurately describe the behavior of particles moving at high speeds or in strong gravitational fields. In these situations, more complex equations, such as the Dirac equation, are used.

5. How does Schrodingers Equation relate to the famous "Schrödinger's cat" thought experiment?

The "Schrödinger's cat" thought experiment was proposed by Erwin Schrödinger to illustrate the bizarre nature of quantum mechanics. It involves a cat in a sealed box with a vial of poison, a radioactive substance, and a Geiger counter. According to the equation, the cat would be both alive and dead until the box is opened and the outcome is observed, reflecting the concept of superposition in quantum mechanics.

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