Boost Your Understanding of De Broglie Equation with Our Examples

The mass of an electron is $9.1\times <!--\; \times \; -->{10}^{-<!--\; -\; -->31}$ kg. If its K.E. is $3.0\times <!--\; \times \; -->{10}^{-<!--\; -\; -->25}J$, calculate its wavelength.

Find the de Broglie wavelength of a football of mass 0.4 kg traveling 23 m/s?

Schrodinger's equation (explanation to non physicist)
For a report I'm writing on Quantum Computing, I'm interested in understanding a little about this famous equation. I'm an undergraduate student of math, so I can bear some formalism in the explanation. However I'm not so stupid to think I can understand this landmark without some years of physics. I'll just be happy to be able to read the equation and recognize it in its various forms.
To be more precise, here are my questions.
Hyperphysics tell me that Shrodinger's equation "is a wave equation in terms of the wavefunction".
1. Where is the wave equation in the most general form of the equation?
$\mathrm{i}\mathrm{\hslash <!--\; \hslash \; -->}\frac{\mathrm{\partial <!--\; \partial \; -->}}{\mathrm{\partial <!--\; \partial \; -->}t}\mathrm{\Psi <!--\; \Psi \; -->}=H\mathrm{\Psi <!--\; \Psi \; -->}$
I thought wave equation should be of the type
$\frac{{\mathrm{\partial <!--\; \partial \; -->}}^2}{{\mathrm{\partial <!--\; \partial \; -->}}^{2}t}u=c^2{\mathrm{\nabla <!--\; \nabla \; -->}}^{2}u$
It's the difference in order of of derivation that is bugging me.
2. Can somebody show me the passages in a simple (or better general) case?
3.I think this questions is the most difficult to answer to a newbie. What is the Hamiltonian of a state? How much, generally speaking, does the Hamiltonian have to do do with the energy of a state?
4.What assumptions did Schrödinger make about the wave function of a state, to be able to write the equation? Or what are the important things I should note in a wave function that are basilar to proof the equation? With both questions I mean, what are the passages between de Broglie (yes there are these waves) and Schrödinger (the wave function is characterized by)?
5.It's often said "The equation helps finds the form of the wave function" as often as "The equation helps us predict the evolution of a wave function" Which of the two? When one, when the other?

To determine
To Describe: A method to measure energy of a photon.

10. In de Broglie's equation, he shows the relationship between the wavelength of a light wave and its momentum. Which of the following is true about this relationship?
1. wavelength is directly proportional to the square of momentum
2. wavelength is inversely proportional to momentum
3. wavelength is directly proportional to momentum
4. wavelength is inversely proportional to the square of momentum

Davisson and Germer scattered electrons from a crystal of nickel. The scattered electrons formed a strong diffraction pattern. What important conclusion was drawn from this experiment?

What is the wavelength (in meters) of a 0.5 kg particle moving with a velocity of $6.63\times <!--\; \times \; -->{10}^{-<!--\; -\; -->34}m/s$?
HINT: Use de Broglie equation with the plank constant in units of $J\cdot <!--\; \cdot \; -->s(h=6.63\times <!--\; \times \; -->{10}^{-<!--\; -\; -->34}Js)$

In an electron microscope, through approximately how many volts of potential difference must electrons be accelerated to achieve a de Broglie wavelength of $1.0\times <!--\; \times \; -->{10}^{-<!--\; -\; -->10}m$?
a) $1.5\times <!--\; \times \; -->{10}^{-<!--\; -\; -->2}V$
b) $1.5\times <!--\; \times \; -->{10}^{-<!--\; -\; -->1}V$
c) $1.5V$
d) $15V$
e) $150V$

In de Broglie's equation w=wavelength, $w=\frac{h}{mv}$. How do I rearrange to solve for mass?

Please explain in detail with steps how to set up and solve for this equation.
Find the de Broglie wavelength for a 1500kg car when its speed is 80km/h. How significant are the wave properties of this car likely to be?

To determine
To Calculate: Momentum of photon by using equation $p=mv$

Calculate the de Broglie wavelength of electrons accelerated through 3868 V. Round off the answer to 2 decimal places with scientific representation.

Factor 2 in Heisenberg Uncertainty Principle: Which formula is correct?
Some websites and textbooks refer to
$\mathrm{\Delta <!--\; \Delta \; -->}x\mathrm{\Delta <!--\; \Delta \; -->}p\ge <!--\; \ge \; -->\frac{\mathrm{\hslash <!--\; \hslash \; -->}}{2}$
as the correct formula for the uncertainty principle whereas other sources use the formula
$\mathrm{\Delta <!--\; \Delta \; -->}x\mathrm{\Delta <!--\; \Delta \; -->}p\ge <!--\; \ge \; -->\mathrm{\hslash <!--\; \hslash \; -->}.$
Question: Which one is correct and why?
The latter is used in the textbook "Physics II for Dummies" (German edition) for several examples and the author also derives that formula so I assume that this is not a typing error.
This is the mentioned derivation:
$\sin <!--\; \; -->\mathrm{\theta <!--\; \theta \; -->}=\frac{\mathrm{\lambda <!--\; \lambda \; -->}}{\mathrm{\Delta <!--\; \Delta \; -->}y}$
assuming $\mathrm{\theta <!--\; \theta \; -->}$ is small:
$\tan <!--\; \; -->\mathrm{\theta <!--\; \theta \; -->}=\frac{\mathrm{\lambda <!--\; \lambda \; -->}}{\mathrm{\Delta <!--\; \Delta \; -->}y}$
de Broglie equation:
$\mathrm{\lambda <!--\; \lambda \; -->}=\frac{h}{p_x}$
$\Rightarrow <!--\; \Rightarrow \; -->\tan <!--\; \; -->\mathrm{\theta <!--\; \theta \; -->}\approx <!--\; \approx \; -->\frac{h}{p_x\cdot <!--\; \cdot \; -->\mathrm{\Delta <!--\; \Delta \; -->}y}$
but also:
$\tan <!--\; \; -->\mathrm{\theta <!--\; \theta \; -->}=\frac{\mathrm{\Delta <!--\; \Delta \; -->}{p}_y}{p_x}$
equalize $\tan <!--\; \; -->\mathrm{\theta <!--\; \theta \; -->}$:
$\frac{h}{p_x\cdot <!--\; \cdot \; -->\mathrm{\Delta <!--\; \Delta \; -->}y}\approx <!--\; \approx \; -->\frac{\mathrm{\Delta <!--\; \Delta \; -->}{p}_y}{p_x}$
$\Rightarrow <!--\; \Rightarrow \; -->\frac{h}{\mathrm{\Delta <!--\; \Delta \; -->}y}\approx <!--\; \approx \; -->\mathrm{\Delta <!--\; \Delta \; -->}{p}_y\Rightarrow <!--\; \Rightarrow \; -->\mathrm{\Delta <!--\; \Delta \; -->}{p}_y\mathrm{\Delta <!--\; \Delta \; -->}y\approx <!--\; \approx \; -->h$
$\Rightarrow <!--\; \Rightarrow \; -->\mathrm{\Delta <!--\; \Delta \; -->}{p}_y\mathrm{\Delta <!--\; \Delta \; -->}y\ge <!--\; \ge \; -->\frac{h}{2\mathrm{\pi <!--\; \pi \; -->}}$
$\Rightarrow <!--\; \Rightarrow \; -->\mathrm{\Delta <!--\; \Delta \; -->}p\mathrm{\Delta <!--\; \Delta \; -->}x\ge <!--\; \ge \; -->\frac{h}{2\mathrm{\pi <!--\; \pi \; -->}}$

To determine
A detailed explanation behind larger atomic size with larger Planck’s constant, h.

Consider a proton with a 6.6 fm wavelength. What is the velocity of the proton in meters per second? Assume the proton is nonrelativistic. (1 femtometer $={10}^{-<!--\; -\; -->15}$ m)

Using dimensional analysis, predict the units of wavelength in the de Broglie hypothesis equation: $\mathrm{\lambda <!--\; \lambda \; -->}=\frac{h}{mv}$
joule-seconds ($J\cdot <!--\; \cdot \; -->s$)
kilogram (kg)
meters (m)
seconds (s)
meters per second (m/s)
per second (/s)
per meter (/m)
per kilogram (/kg)

At what velocity will an electron have a wavelength of 1.00 m?

If matter has a wave nature, why is this wave - like characteristic not observable in our daily experiences?

In the Davisson-Germer experiment using a nickel crystal, a second-order beam is observed at an angle of 55 degrees. For what value of acclerating voltage does this occur?

Why wave nature of particles is not observed in daily life.