# Introduction to Quantum Mechanics

## History of Quantum Mechanics

History of Quantum Mechanics

### Quantum Mechanics was first derived to explain why classical (Newtonian) mechanics did not explain experimental data on very small scales.

Quantum Mechanics was first derived to explain why classical (Newtonian) mechanics did not explain experimental data on very small scales.

### Quantum Theory first began to be described in the early 20th century, and forms one of the three key explanations of the physical properties of the Universe (General Relativity and classical mechanics being the other two...)

Quantum Theory first began to be described in the early 20th century, and forms one of the three key explanations of the physical properties of the Universe (General Relativity and classical mechanics being the other two...)

### Many of the scientists involved with the development of Quantum Theory have become household names with their theories even entering pop culture, so great was the impact of Quantum Theory.

Many of the scientists involved with the development of Quantum Theory have become household names with their theories even entering pop culture, so great was the impact of Quantum Theory.

### Quantum Mechanics predicts the behaviour and properties of subatomic particles and is the basis of our understanding of lasers and microchips. Without Quantum Mechanics, it is not possible to even explain why matter exists at all...

Quantum Mechanics predicts the behaviour and properties of subatomic particles and is the basis of our understanding of lasers and microchips. Without Quantum Mechanics, it is not possible to even explain why matter exists at all...

### The image shown below was taken at the 5^{th} Solvay Conference in 1927 at which the newly formulated Quantum Theory was first discussed. This image has been called "The most intelligent photograph of all time".

The image shown below was taken at the 5

^{th}Solvay Conference in 1927 at which the newly formulated Quantum Theory was first discussed. This image has been called "The most intelligent photograph of all time".

### In this single image can be seen 30 of the most highly respected Scientists of modern times, with 17 of the attendees achieving at least one Nobel Prize.

In this single image can be seen 30 of the most highly respected Scientists of modern times, with 17 of the attendees achieving at least one Nobel Prize.

### The timeline below shows some of the key points in the development of Quantum Mechanics :-

The timeline below shows some of the key points in the development of Quantum Mechanics :-

## Difficulties with Newtonian ( Classical ) Mechanics

Difficulties with Newtonian ( Classical ) Mechanics

### Quantum Theory grew out of a need to explain limitations found within classical mechanics theory. For most everyday situations, classical mechanics accurately predicts or explains experimental evidence. However, when observations are made over very small or very short scales, classical mechanics starts to have difficulties.

Quantum Theory grew out of a need to explain limitations found within classical mechanics theory. For most everyday situations, classical mechanics accurately predicts or explains experimental evidence. However, when observations are made over very small or very short scales, classical mechanics starts to have difficulties.

### The following is a discussion of the major issues within classical mechanics that Quantum Theory can provide a solution to.

The following is a discussion of the major issues within classical mechanics that Quantum Theory can provide a solution to.

## Blackbody Radiation and the Ultraviolet Catastrophe

Blackbody Radiation and the Ultraviolet Catastrophe

### In the late 19th century, scientists were attempting to understand the colour changes of metals as they were heated. In order to investigate this as accurately as possible, the concept of an ideal emitter of radiation called a Blackbody object, was devised. The continuous spectrum produced by a Blackbody object is known as Blackbody Radiation.

In the late 19th century, scientists were attempting to understand the colour changes of metals as they were heated. In order to investigate this as accurately as possible, the concept of an ideal emitter of radiation called a Blackbody object, was devised. The continuous spectrum produced by a Blackbody object is known as Blackbody Radiation.

### Measurements of the intensity of light emitted at different wavelengths were made and the results showed that the radiation emitted depended not on the material used, but only on the temperature of the object.

Measurements of the intensity of light emitted at different wavelengths were made and the results showed that the radiation emitted depended not on the material used, but only on the temperature of the object.

### The diagram below shows the Intensity of emitted radiation from a Blackbody object over a range of Wavelengths at various temperatures :-

The diagram below shows the Intensity of emitted radiation from a Blackbody object over a range of Wavelengths at various temperatures :-

### As can been seen above, as the temperature of the object increases, the maximum of the curve moves towards the lower (more blue) wavelengths. This is seen as the colour changes in the Blackbody object.

As can been seen above, as the temperature of the object increases, the maximum of the curve moves towards the lower (more blue) wavelengths. This is seen as the colour changes in the Blackbody object.

### However, when scientists attempted to explain this shift in Wavelength with Temperature, they ran into large problems. Wilhelm Wein managed to derive an equation that explained the high frequency sections well, but not the low frequency sections. Lord Rayleigh then derived an equation to explain the low frequency sections, but as the frequency increased, this equation tended to infinite energy being emitted (referred to as the Ultraviolet Catastrophe) . This can be seen in the above graph as the exponential curve tending to infinity as the Wavelength tends to zero.

However, when scientists attempted to explain this shift in Wavelength with Temperature, they ran into large problems. Wilhelm Wein managed to derive an equation that explained the high frequency sections well, but not the low frequency sections. Lord Rayleigh then derived an equation to explain the low frequency sections, but as the frequency increased, this equation tended to infinite energy being emitted (referred to as the Ultraviolet Catastrophe) . This can be seen in the above graph as the exponential curve tending to infinity as the Wavelength tends to zero.

### This issue failed to be resolved through classical mechanics, and it was only through Max Plank's work on Quantum Mechanics that this was resolved.

This issue failed to be resolved through classical mechanics, and it was only through Max Plank's work on Quantum Mechanics that this was resolved.

### Plank examined the two equations, trying to combine them together, but found that if the light was modeled as a wave, the issues could not be resolved. Plank decided that the only way to create a model that explains the observed data was to treat light not as a continuous wave, but as quantised energy values.

Plank examined the two equations, trying to combine them together, but found that if the light was modeled as a wave, the issues could not be resolved. Plank decided that the only way to create a model that explains the observed data was to treat light not as a continuous wave, but as quantised energy values.

### This model gave Einstein the groundwork for his development of Photon theory of light, and allows scientists to clearly understand the emitted light curves from a Blackbody object.

This model gave Einstein the groundwork for his development of Photon theory of light, and allows scientists to clearly understand the emitted light curves from a Blackbody object.

### Note - In the above explanation, it is Plank's model of a "Quantum of Energy" that provides the name of this entire branch of Physics - Quantum Mechanics.

Note - In the above explanation, it is Plank's model of a "Quantum of Energy" that provides the name of this entire branch of Physics - Quantum Mechanics.

## The Photoelectric Effect

The Photoelectric Effect

### As stated above Einstein used Plank's concept of quantised energy to explain his observations of the Photoelectric Effect.

As stated above Einstein used Plank's concept of quantised energy to explain his observations of the Photoelectric Effect.

### When photons of ultra-violet radiation are shone onto the zinc plate, they have sufficient energy to eject electrons from the surface of the zinc. White light does not have sufficient energy, no matter the brightness, and so the Electroscope does not discharge.

When photons of ultra-violet radiation are shone onto the zinc plate, they have sufficient energy to eject electrons from the surface of the zinc. White light does not have sufficient energy, no matter the brightness, and so the Electroscope does not discharge.

### If Light was behaving as a Wave, increasing the brightness of white light should have given sufficient energy to eject electrons, but this does not work.

If Light was behaving as a Wave, increasing the brightness of white light should have given sufficient energy to eject electrons, but this does not work.

### The only way to explain the above observations is that light is behaving as a particle, as only a Photon of sufficient energy can cause the ejection of an electron. Therefore the Photoelectric Effect "proves" light is a quantised energy packet.

The only way to explain the above observations is that light is behaving as a particle, as only a Photon of sufficient energy can cause the ejection of an electron. Therefore the Photoelectric Effect "proves" light is a quantised energy packet.

### Note - For further information on the Photoelectric Effect, please see Higher Physics Photoelectric Effect.

Note - For further information on the Photoelectric Effect, please see Higher Physics Photoelectric Effect.