Schrodinger wave equation

6.1 Derivation of the Schr¨odinger Wave Equation

6.1.1 The Time Dependent Schr¨odinger Wave Equation

In the discussion of the particle in an infinite potential well, it was observed that the wave function of a particle of fixed energy E could most naturally be written as a linear combination of wave functions of the form

Ψ(x,t) = Aei(kx−ωt) (6.1)

representing a wave travelling in the positive x direction, and a corresponding wave travelling in the opposite direction, so giving rise to a standing wave, this being necessary in order to satisfy the boundary conditions. This corresponds intuitively to our classical notion of a particle bouncing back and forth between the walls of the potential well, which suggests that we adopt the wave function above as being the appropriate wave function

Chapter 6 The Schr¨odinger Wave Equation 43

for a free particle of momentum p = !k and energy E = !ω. With this in mind, we can then note that ∂2Ψ ∂x2 =−k2Ψ (6.2) which can be written, using E = p2/2m = !2k2/2m:

!2 2m

∂2Ψ ∂x2

= p2 2m

Ψ. (6.3)

Similarly

∂Ψ ∂t

=−iωΨ (6.4)

which can be written, using E = !ω: i!∂Ψ ∂t

= !ωψ = EΨ. (6.5)

We now generalize this to the situation in which there is both a kinetic energy and a potential energy present, then E = p2/2m+V(x) so that EΨ = p2 2m Ψ+V(x)Ψ (6.6) where Ψ is now the wave function of a particle moving in the presence of a potential V(x). But if we assume that the results Eq. (6.3) and Eq. (6.5) still apply in this case then we have − !2 2m ∂2ψ ∂x2 +V(x)Ψ = i!∂ψ ∂t (6.7) which is the famous time dependent Schr¨odinger wave equation.

Curiously enough, to answer this question requires ‘extracting’ the time dependence from the time dependent Schr¨odinger equation. To see how this is done, and its consequences, we will turn our attention to the closely related time independent version of this equation.

KINETICS AND MECHANISMS OF INORGANIC REACTIONS

As is usual in these Reports it is only possible to mention a proportion, here about a quarter, of the year’s relevant references. In the process of selection all references to two active fields which overlap organic chemistry, organo-silicon and -germanium chemistry, and oxidations of organic com- pounds by inorganic species, have been eliminated. The emphasis on reactions of transition-metal complexes in this Report reflects the continued major interest in this aspect of inorganic kinetics. [Throughout this Report L stands for any ligand, as specified in the text, X stands for a halogen atom ((31, Br, I) unless otherwise stated, and AH$ and A$ represent enthalpies and entropies of activation. References to the Russian literature quote page numbers of the English translations.] Redox Reactions.-There has again been much work on inner-sphere reductions of cobalt(m) Complexes by chromium(@. cis-[Co(en),(N,),]+ and cis-[Co(NHC,),(N,),]+ react by parallel paths involving a single or a double azide bridge.l For [Co(en>,(NCS)Xln+ (X = C1, NCS, NH,, OH,) chrom- [email protected]) attack can occur at either nitrogen or sulphur to form the thiocyanate bridge., The importance of steric factors and ligand reducibility have been investigated for reduction of thirty carboxylatopenta-amminecobalt(m) complexes ; for aromatic carboxylate ligands containing anitro group there is evidence for chromium(n) attack at the nitro group.3 The rate of ring closure of [Cr( OH2),( O,C*CH,*CO,H)] ,+, containing unidentate malonate, to the chelate [Cr( OH2),( O,C*CH,*CO,)] + is much slower than the rate of reduc- tion of [Co(NH,),( 02C*CH2*C02H)]2+ by chromium(n) .4 This evidence, together with rate constants and product distribution from analogous reduc- tions of malonate half-ester c~mplexes,~ refutes the earlier postulate of chromium(@ attack at the remote oxygen atom of the malonate ligand. The transition state now suggested contains chromium bonded to oxygen atoms from both carboxyl groups of the bridging malonate. The nature of intermediates in the chromium( 11) reduction of nicotinamido- and isonicotin- amido-penta-amminecobalt(m) casts further doubt on the general applica- bility of the remote attack hypothesis.6 Reaction rates of chromium(I1) with cis- and truns-[Co(en),(OH2),]3+ and [Co(en),(OH2)(NH,)33f indicate a trans effect, though this is much less marked than for reduction by iron

How to Access DarkWeb

◼️Steps

⭕️There are many ways to access the dark web. Being a part of the deep net, dark web operates differently than the clear-net, and needs special client software to be accessed. While there are multiple ways to access the dark web, the most common and recommended method involves using TOR, and then visiting the .onion websites. All dark web website have a URL with .onion domain, which looks similar to the way the clear-net websites have .com, .org, .net, etc. Once you have TOR and find out the .onion address of a deep web site (hidden web site),you can simply enter it in the URL bar on TOR browser, and it’ll open, just as normal websites open in usual browsers.

⭕️ If you read the previous boring section, you’d see that I mentioned how the dark net often uses uncommon communication protocols, etc. In case of the dark web, we see that phenomenon with respect to the onion websites. I won’t go in much depth, but first look at a .onion URL suggests that it’s similar to the clear-net websites. However, internally, the way they work is nothing similar to the clear-net. Precisely, .onion is not part of the internet’s DNS root, and hence, normal DNS servers can’t resolve your request if you type the URL of a .onion website on your browser. TOR redirects these requests through it’s own servers, similar to the way proxies work, and then we get to the website, without the involvement of DNS servers anywhere. This ensures that search engine bots can’t browse around the deep web, and that anonymity is maintained, both of the client looking at the web pages, as well as the server serving the web pages (In other words, the server doesn’t know who the client is, and the client doesn’t know anything about where the server is.)

Ⓜ️If you’re using Windows, you can download the Tor executable on web..versions for linux and mac available also you can use in your android device but it’s not safe

Types of Hackers

🔰Miscellaneous Hackers🔰

Apart from few well known class hackers , we have following categories of hackers based on what they hack and how they do it-

🔴RED HAT HACKERS: Red hat hackers are blend of both black hat and white hat hackers . They are usually on the level of Hacking government agencies , top secret information hubs and generally anything that falls under the category of sensitive information.

🔵Blue hat hackers: A blue hat hacker is someone outside computer security consulting firms who bug tests a system prior to its launch, looking for exploits so they can be closed. Blue Hat Hacker also refers to the security professional invited by Microsoft to find vulnerabilities in Windows.

🔴Elite Hackers: Elite hacker is the name utilized by the community with the aim of identifying those individuals who are deemed to be as experts in their line of work. These people are actually on the “cutting edge” of both the computer and network industry.

🔴Script Kiddie : script kiddie or skiddie is an unskilled individual who uses scripts or programs developed by others to attack computer systems and networks and deface websites.

🔴Neophyte: Someone who is new to Hacking or phreaking and has almost no knowledge or experience of the workings of technology and Hacking.

🔴Hactivist : A hacker who utilizes technology to announce a social , ideological , religious or political message . In general , most hactivism involves website defacement or denial-of-service attacks. 💢

List of terms used in the field of hacking

List of terms used in the field of hacking.

Adware − Adware is software designed to force pre-chosen ads to display on your system.

Attack − An attack is an action that is done on a system to get its access and extract sensitive data.

Back door − A back door, or trap door, is a hidden entry to a computing device or software that bypasses security measures, such as logins and password protections.

Bot − A bot is a program that automates an action so that it can be done repeatedly at a much higher rate for a more sustained period than a human operator could do it. For example, sending HTTP, FTP or Telnet at a higher rate or calling script to create objects at a higher rate.

Botnet − A botnet, also known as zombie army, is a group of computers controlled without their owners’ knowledge. Botnets are used to send spam or make denial of service attacks.

Brute force attack − A brute force attack is an automated and the simplest kind of method to gain access to a system or website. It tries different combination of usernames and passwords, over and over again, until it gets in.

Buffer Overflow − Buffer Overflow is a flaw that occurs when more data is written to a block of memory, or buffer, than the buffer is allocated to hold.

Clone phishing − Clone phishing is the modification of an existing, legitimate email with a false link to trick the recipient into providing personal information.

Cracker − A cracker is one who modifies the software to access the features which are considered undesirable by the person cracking the software, especially copy protection features.

Denial of service attack (DoS) − A denial of service (DoS) attack is a malicious attempt to make a server or a network resource unavailable to users, usually by temporarily interrupting or suspending the services of a host connected to the Internet.

DDoS − Distributed denial of service attack.

Exploit Kit − An exploit kit is software system designed to run on web servers, with the purpose of identifying software vulnerabilities in client machines communicating with it and exploiting discovered vulnerabilities to upload and execute malicious code on the client.

Exploit − Exploit is a piece of software, a chunk of data, or a sequence of commands that takes advantage of a bug or vulnerability to compromise the security of a computer or network system.

Firewall − A firewall is a filter designed to keep unwanted intruders outside a computer system or network while allowing safe communication between systems and users on the inside of the firewall.

Keystroke logging − Keystroke logging is the process of tracking the keys which are pressed on a computer (and which touchscreen points are used). It is simply the map of a computer/human interface. It is used by gray and black hat hackers to record login IDs and passwords. Keyloggers are usually secreted onto a device using a Trojan delivered by a phishing email.

Logic bomb − A virus secreted into a system that triggers a malicious action when certain conditions are met. The most common version is the time bomb.

Malware − Malware is an umbrella term used to refer to a variety of forms of hostile or intrusive software, including computer viruses, worms, Trojan horses, ransomware, spyware, adware, scareware, and other malicious programs.

Master Program − A master program is the program a black hat hacker uses to remotely transmit commands to infected zombie drones, normally to carry out Denial of Service attacks or spam attacks.

Phishing − Phishing is an e-mail fraud method in which the perpetrator sends out legitimate-looking emails, in an attempt to gather personal and financial information from recipients.

Phreaker − Phreakers are considered the original computer hackers and they are those who break into the telephone network illegally, typically to make free longdistance phone calls or to tap phone lines.